Page i
Risk Management
Michel Crouhy
Dan Galai
Robert Mark

Page v
Contents
Foreword xiii
By Robert C. Merton
Introduction xvii
By John Hunkin
Preface xix
Chapter 1 1
The Need for Risk Management Systems
1. Introduction 1
2. Historical Evolution 4
3. The Regulatory Environment 19
4. The Academic Background and Technological Changes 21
5. Accounting Systems versus Risk Management Systems 29
6. Lessons from Recent Financial Disasters 31
7. Typology of Risk Exposures 34
8. Extending Risk Management Systems to Nonfinancial 39
Corporations
Notes 41
Chapter 2 45
The New Regulatory and Corporate Environment
1. Introduction 45
2. The Group of 30 (G-30) Policy Recommendations 48
3. The 1988 BIS Accord: The "Accord" 53
4. The "1996 Amendment" or "BIS 98" 62
5. The BIS 2000+ Accord 68
Notes 91
Chapter 3 97
Structuring and Managing the Risk Management Function in a Bank
1. Introduction 97
2. Organizing the Risk Management Function: Three-Pillar 99
Framework

Page vi
3. Data and Technological Infrastructure 109
4. Risk Authorities and Risk Control 116
5. Establishing Risk Limits for Gap and Liquidity Management 126
6. Conclusion: Steps to Success 133
Notes 135
Chapter 4 137
The New BIS Capital Requirements for Financial Risks
1. Introduction 137
2. The Standardized Approach 138
3. The Internal Models Approach 150
4. Pros and Cons of the Standardized and Internal Models 162
Approaches: A New Proposal—the "Precommitment Approach"
5. Comparisons of the Capital Charges for Various Portfolios 165
According to the Standardized and the Internal Models Approaches
6. Conclusions 169
Notes 174
Chapter 5 177
Measuring Market Risk: The VaR Approach
1. Introduction 177
2. Measuring Risk: A Historical Perspective 179
3. Defining Value at Risk 187
4. Calculating Value at Risk 196
5. Conclusion: Pros and Cons of the Different Approaches 216
Appendix 1: Duration and Convexity of a Bond 218
Notes 225
Chapter 6 229
Measuring Market Risk: Extensions of the VaR Approach and Testing
the Models
1. Introduction 229
2. Incremental-VaR (IVAR), DeltaVar (DVAR), and Most 230
Significant Risks
3. Stress Testing and Scenario Analysis 232

Page vii
4. Dynamic-VaR 241
5. Measurement Errors and Back-Testing of VaR Models 243
6. Improved Variance-Covariance VaR Model 249
7. Limitations of VaR as a Risk Measure 252
Appendix: Proof of the Deltavar Property 255
Notes 257
Chapter 7 259
Credit Rating Systems
1. Introduction 259
2. Rating Agencies 261
3. Introduction to Internal Risk Rating 269
4. Debt Rating and Migration 275
5. Financial Assessment (Step 1) 282
6. First Group of Adjustment Factors for Obligor Credit Rating 290
7. Second Group of Adjustment Factors for Facility Rating 298
8. Conclusion 301
Appendix 1: Definitions of Key Ratios 302
Appendix 2: Key Financial Analysis Measures 303
Appendix 3A: Prototype Industry Assessment: Telecommunications in Canada 306
Appendix 3B: Prototype Industry Assessment: Footwear and Clothing in Canada 308
Appendix 4: Prototype Country Analysis Report (Condensed Version): Brazil 310
Notes 312

Chapter 8 315
Credit Migration Approach to Measuring Credit Risk
1. Introduction 315
2. CreditMetrics Framework 319
3. Credit VaR for a Bond (Building Block 1) 321
4. Credit VaR for a Loan or Bond Portfolio (Building Block 2) 329
5. Analysis of Credit Diversification (Building Block 2, Continuation) 338
6. Credit VaR and the Calculation of the Capital Charge 339

Page viii
7. CreditMetrics as a Loan/Bond Portfolio Management Tool: Marginal Risk Measures 340
(Building Block 2, Continuation)
8. Estimation of Asset Correlations (Building Block 3) 342
9. Exposures (Building Block 4) 343
10. Conditional Transition Probabilities: CreditPortfolioView 344
11. Appendix 1: Elements of Merton's Model 347
Appendix 2: Default Prediction—The Econometric Model 350
Appendix 3: Transition Matrix over a Period of Less than One Year 352
Notes 352
Chapter 9 357
The Contingent Claim Approach to Measuring Credit Risk
1. Introduction 357
2. A Structural Model of Default Risk: Merton's (1974) Model 360
3. Probability of Default, Conditional Expected Recovery Value, and Default Spread 364
4. Estimating Credit Risk as a Function of Equity Value 366
5. KMV Approach 368
6. KMV's Valuation Model for Cash Flows Subject to Default Risk 381
7. Asset Return Correlation Model 384
Appendix 1: Integrating Yield Spread with Options Approach 389
Appendix 2: Risk-Neutral Valuation Using "Risk-Neutral" EDFs 392
Appendix 3: Limitations of the Merton Model and Some Extensions 395
Notes 399

Chapter 10 403
Other Approaches: The Actuarial and Reduced-Form Approaches to Measuring Credit Risk
1. Introduction 403
2. The Actuarial Approach: CreditRisk+ 404
3. The Reduced-Form Approach or Intensity-Based Models 411
Notes 422

Page ix
Chapter 11 425
Comparison of Industry-Sponsored Credit Models and Associated Back-Testing Issues
1. Introduction 425
2. Comparison of Industry-Sponsored Credit Risk Models 427
3. Stress Testing and Scenario Analysis 430
4. Implementation and Validation Issues 436
Notes 438
Chapter 12 441
Hedging Credit Risk
1. Introduction 441
2. Credit Risk Enhancement 443
3. Derivative Product Companies 446
4. Credit Derivatives 448
5. Types of Credit Derivatives 452
6. Credit Risk Securitization for Loans and High Yield Bonds 461
7. Regulatory Issues 466
Notes 470
Chapter 13 475
Managing Operational Risk
1. Introduction 475
2. Typology of Operational Risks 478
3. Who Should Manage Operational Risk? 482
4. The Key to Implementing Bank-Wide Operational Risk Management 486

5. A Four-Step Measurement Process for Operational Risk 489
6. Capital Attribution for Operational Risks 505
7. Self-Assessment versus Risk Management Assessment 509
8. Integrated Operational Risk 511
9. Conclusion 513
Appendix 1: Group of Thirty Recommendations: Derivatives and Operational Risk 514
Appendix 2: Types of Operational Risk Losses 518

Page x
Appendix 3: Severity versus Likelihood 519
Appendix 4: Training and Risk Education 519
Appendix 5: Identifying and Quantifying Operational Risk 523
Notes 526
Chapter 14 529
Capital Allocation and Performance Measurement
1. Introduction 529
2. Guiding Principles of RAROC Implementation 538
3. Relationship of RAROC Capital to Market, Credit, and Operational Risks 543
4. Loan Equivalent Approach 549
5. Measuring Exposures and Losses for Derivatives 551
6. Measuring Risk Adjusted Performance: Second Generation of RAROC Model 559
7. Concluding Remarks 566
Appendix 1: First Generation of RAROC Model—Assumptions in Calculating Exposures, 570
Expected Default, and Expected Losses
Notes 577
Chapter 15 579
Model Risk
1. Introduction 579
2. Valuation Models and Sources of Model Risk 581
3. Typology of Model Risks 585
4. What Can Go Wrong? 594
5. What Can Market Risk Management Do to Mitigate Model Risk? 606

6. Conclusions 610
Notes 611
Chapter 16 615
Risk Management in Nonbank Corporations
1. Introduction 615
2. Why Manage Risks? 617

Page xi
3. Procedure for Risk Management 622
4. Accounting Reports 630
5. Reporting Requirements by Securities Authorities 634
Appendix 1: Examples of Reports on Risk Exposure by Nike, Merck, and Microsoft, 1988 645
Notes 659
Chapter 17 661
Risk Management in the Future
1. The Total Risk-Enabled Bank 661
2. External Client Profitability . . . A Partner PlusTM Approach 669
3. Process for Reviewing Risk in Extreme Markets Will Become Standardized 674
4. The Credit Analysis Process and the Need for Integrating Risks 678
5. An Idealized Bank of the Future 684
Appendix: The Relationship between Market Risk, Business Risk, and Credit Risk 685
Notes 690
References 693
Index 709

Page xiii
Foreword
Risk is the fundamental element that influences financial behavior. In its absence, the financial
system necessary for efficient allocations of resources would be vastly simplified. In that world, only
a few institutions and financial instruments would be needed, and the practice of finance would
require relatively elementary analytical tools. But, of course, in the real world, risk is ubiquitous.
Much of the structure of the financial system we see serves the function of the efficient distribution
of risk. Much of the financial decision making by households, business firms, governments, and
especially financial institutions is focused on the management of risk. Measuring the influence of
risk, and analyzing ways of controlling and allocating it, require a wide range of sophisticated
mathematical and computational tools. Indeed, mathematical models of modern finance practice
contain some of the most complex applications of probability, optimization, and estimation theories.
Those applications challenge the most powerful of computational technologies.
Risk Management provides a comprehensive introduction to the subject. Presented within the
framework of a financial institution, it covers the design and operation of a risk-management system,
the technical modeling within that system, and the interplay between the internal oversight and the
external regulatory components of the system. That its authors, Michel Crouhy, Dan Galai, and
Robert Mark, are significant contributors to the science of finance, active practitioners of finance, and
experienced teachers of finance is apparent from both its substance and form. The range of topics is
broad but evidently carefully chosen for its applicability to practice. The mathematical models and
methodology of risk management are presented rigorously, and they are seamlessly integrated with
the empirical and clinical evidence on their applications. The book also patiently provides readers
without an advanced mathematical background the essential analytical foundations of risk
management.
The opening four chapters provide a fine introduction to the function of the risk management system
within the institution and

Page xiv
on the management of the system itself. Recent regulatory trends are presented to illustrate the
expanded role that the internal system plays in informing and meeting the requirements of the
external overseers of the institution.
With this as background, the book turns to the core substance of a risk management system with the
analysis and modeling of risk measurement and control. Market risk is the first topic explored,
including the ubiquitous VaR models and stress testing for identifying and measuring risk exposures
to stock market, interest rate, currency, and commodity prices. The analysis shows how to
incorporate option, derivative and other ''nonlinear" security exposures into those models.
Nearly a third of the book is devoted to the management of credit risk, and for good reason. Banks
are in the business of making loans and they also issue guarantees of financial performance for their
customers. They enter into bilateral contractual agreements such as swaps, forward contracts, and
options on enormous scales that expose them to the risk that their counterparts to those contracts will
not fulfill their obligations. Similarly, insurance companies hold corporate bonds that may default and
some guarantee the performance of bonds issued by municipal governments. The credit derivatives
business is one of the fastest growing areas for financial products. However, credit risk analysis has
even greater importance to risk management in its application to the soundness of the institution
itself. Indeed, for financial institutions with principal businesses, which involve issuing contingent-
payment contracts such as deposits, annuities, and insurance to their customers, creditworthiness is
the central financial issue. The mere prospect of a future default by an institution on its customer
obligations can effectively destroy those businesses. Unlike investors in an institution, its customers
do not want to bear its credit risk, even for a price. The book presents the major competing models
for measuring and valuing credit risk and evaluates them, both theoretically and empirically.
In addition to market and credit risk exposures, a comprehensive approach to risk measurement and
risk management must also include operational risks, which is the subject of Chapter 13.
Furthermore, no risk management system can be effective without well-designed performance
measurement and testing. This is

Page xv
needed both to estimate the risk exposures ex ante and to provide an ex post assessment of those
estimates relative to predictions, as a feedback on the performance of the system. As laid out in
Chapter 14, the system's risk estimates provide the basis for capital attribution among the activities
and the accuracy of those estimates determine the amount of equity capital "cushion" needed as a
whole.
Mathematical models of valuation and risk assessment are at the core of modern risk management
systems. Every major financial institution in the world, including sovereign central banks, depends on
these models and none could function without them. Although mainstream and indispensable, these
models are by necessity abstractions of the complex real world. Although there is continuing
improvement in those models, their accuracy as useful approximations to that world varies
significantly across time and situation. Thus, a dimension of risk management that by definition is
outside the formal risk management model is model risk. Chapter 15 explores that issue. It drives
home the point that there is no "safe harbor" in model error, whether complex mathematical models
or traditional measures with rules of thumb. For example, in the case of financial institutions, the
traditional accounting leverage ratio measured by total assets/equity can be cut in half by using a
"borrow-versus-pledge" method to finance security inventory versus using a "repo-reverse repo"
method even though the economic risk of the two methods is identical. Furthermore, the institution
can use derivative securities to greatly alter its measured leverage ratio without changing its economic
risk. The risk-measurement approaches emphasized in the book are ones that give consistent readings
among these different institutional ways of taking on the same risk exposure.
The pace of financial innovation has been extraordinary over the past quarter century and there is no
sign of abatement in either product and service innovation or changes in the institutional structures of
the providers. As discussed in Chapter 16, a major growth area will be in providing integrated risk
management to nonfinancial firms. More generally, from individual households to government users,
the trend in financial services lies with integrated products that are smarter, more comprehensive,
simpler to understand, and more reliable for those users. The future of risk management, as
articulated in Chapter 17, rests in helping the pro-

Page xvi
ducer handle the greater complexity of creating and maintaining those products. The prescriptions
contained herein will age well.
To the reader: Learn and enjoy.
ROBERT C. MERTON
HARVARD BUSINESS SCHOOL

Page xvii
Introduction
The traditional role of the risk manager as corporate steward is evolving as organizations face an
increasingly complex and uncertain future. The mandate to clearly identify, measure, manage, and
control risk has been expanded and integrated into best practice management of a bank. Today's risk
manager is a key member of the senior executive team who helps define business opportunities from
a risk-return perspective, presents unique ways of looking at them, has direct input into the
configuration of products and services, and ensures the transparency of all the risks. Innovation
necessitates new yardsticks for measuring and monitoring the resulting activities. The savvy
corporate leader uses risk management as both a sword and a shield.
At the end of the last millennium, financial institutions and investors experienced increased volatility
in the major financial and commodity markets, with many financial crises. At the start of the new
millennium, we are in the midst of a technological revolution resulting in changes in the operation of
markets, increased access to information, changes in the types of services available to investors, as
well as major changes in the production and distribution of financial services.
If there is concern about an institution's ability to manage risk, then its share price will be penalized.
Risk is a cost of doing business for a financial institution and consequently best practice risk
management is a benefit to our shareholders. To manage the risks facing an institution we must have
a clearly defined set of risk policies and the ability to measure risk. But what do we measure? And
how do we measure such risks? We must also have a best practice infrastructure. The starting point is
that we need a framework.
This book provides such a framework. The content of the book is consistent with our own risk
management strategy and experience. Our risk management strategy is designed to ensure that our
senior management operates together in partnership to control risk while ensuring the independence
of the risk management function. Improvements in analytic models and systems technology have

Page xviii
greatly facilitated our ability to measure and manage risk. However, the new millennium brings new
challenges. There are risks that we can identify and measure and there is the uncertainty of the
unknown. The challenge facing risk managers is to minimize the consequences of the unknown. This
book should help all risk and business managers address the issues arising from risk and uncertainty.
JOHN HUNKIN
CHAIRMAN & CHIEF EXECUTIVE OFFICER
CANADIAN IMPERIAL BANK OF COMMERCE

Page xix
Preface
Risk Management introduces, illustrates, and analyzes the many aspects of modern risk management
in both financial institutions and nonbank corporations. It consolidates the entire field of risk
management from policies to methodologies as well as data and technological infrastructure. It also
covers investment, hedging, and management strategies.
The shift to flexible exchange rates in the late 1960s has led to more volatility in exchange rates. As
volatility increased, financial markets began to offer a new breed of securities, that is, derivatives
such as futures and options, to allow institutions to hedge their exposures to currency fluctuations.
The increase in inflation in the early 1970s and the advent of floating exchange rates soon began to
generate interest rate instability. Again, the market responded by offering new derivative products to
hedge and manage these new risks. Banks found themselves increasingly engaged in risk
intermediation and less in traditional maturity intermediation. Banks also started to innovate and offer
new customized derivative instruments, known as over-the-counter (OTC) products, that both
compete with and complement traded derivatives.
In 1988 the Bank for International Settlements (BIS) set the capital adequacy requirements for
banking worldwide to account for credit risk. This was the first international effort to deal with the
growing exposure of financial institutions to risk and volatilities, and especially to risk of off-balance
sheet claims such as derivative instruments. The 1988 BIS Accord was followed by the 1998 BIS
Accord, accounting for market risks in the trading book, as well as by many documents of the BIS
discussing the many facets of risk management. The SEC implemented its risk exposure disclosure
requirements in 1998 for all exchange traded companies in the United States.
Risk management is not an American phenomenon. Today it covers all continents and all countries.
What we observe today is a convergence of regulation and disclosure requirements across the

Page xx
globe. More than in any other field, the tools and reporting requirements of risk management are
universal.
This book is based on our academic as well as practical work in the field of risk management. We try
to cover both institutional aspects and organizational issues, while not forgetting that risk
management is based on statistical and financial models.
The book is a comprehensive treatment of all aspects of risk management. It starts by discussing the
new regulatory framework that is shaping best practice risk management in the banking industry
worldwide. The risk management techniques that have been developed by and for banks are now
migrating to the corporate sector. There is mounting pressure from regulators, such as the SEC in the
United States, financial analysts, and investors for more and better disclosures of financial risks and
the techniques and instruments being adopted to control these risks.
The book provides a consistent and comprehensive coverage of all aspects of risk management—
organizational structure, methodologies, policies, and infrastructure—for both financial and
nonfinancial institutions. It offers an up-to-date exposition of risk measurement techniques for
market, credit risk, and operational risk. The risk measurement techniques discussed in the book are
based on the latest research. They are presented, however, with considerations based on practical
experience with the daily application of these new risk measurement tools. The book also elaborates
on the issues that the next generation of risk measurement models will have to address, such as the
full integration in a consistent multiperiod framework of liquidity, market, and credit risk; the
measurement of risk for illiquid positions, as for example the merchant banking book; the risk
assessment over a long-term horizon of structural positions, such as the "gap" of the corporate
treasury in a financial institution; and stress testing to assess risk in periods of financial crises.
The book relies heavily on the experience of the authors in developing the risk management function
in a bank from the ground up. It goes beyond the technical aspects of risk measurement. It proposes
an integrated framework for managing risks and an organizational structure that has proven
successful in practice.
We have incorporated the latest evolution of the regulatory framework and the current BIS proposal
to reform the capital

Page xxi
Accord. The book offers a unique presentation of the latest credit risk management techniques. It
provides clear guidance to implement a risk management group in a financial institution. It also
discusses how to adapt to a nonfinancial corporation the risk management techniques that have been
originally developed and implemented in banks. The book provides one-stop shopping for knowledge
in risk management ranging from current regulatory issues, data, technological infrastructure, hedging
techniques, and organizational structure.
Structure of the Book
The book is arranged according to the major subjects of modern risk management. Chapter 1
discusses the need for risk management systems. Chapter 2 presents the new regulatory framework
that is shaping modern risk management in financial institutions and nonbank corporations. Chapter 3
provides an integrated framework for best-practice risk management. We explain how financial
institutions should establish appropriate firm-wide policies, methodologies, and infrastructure in
order to measure, price, and control risks in a comprehensive manner. Chapter 4 reviews the new BIS
capital requirements for market risks and compares the "standardized approach" and the "internal
models approach" that banks can use to report regulatory capital.
The topic of Chapters 5 and 6 is market risk measurement. We present the standard value-at-risk
(VaR) approach. We also discuss some extensions of the VaR method: "incremental-VaR" and
"delta-VaR" to isolate the component risks that contribute most to the total risk, "dynamic-VaR" to
assess market and liquidity risks over a long time horizon, say a quarter, and "E-VaR,'' the expected
loss in the tail, as an alternative risk measure to VaR. We also look at stress testing and scenario
analysis to analyze extreme events that lie outside normal market conditions assumed by the standard
VaR model. Finally, we discuss measurement errors and backtesting issues.
Chapters 7 to 12 cover credit risk. These six chapters constitute a unique and comprehensive
coverage of topical credit risk-related issues: credit risk rating, credit risk measurement with a detailed
presentation of the four industry-sponsored approaches

Page xxii
(credit migration, contingent claim, actuarial, and reduced form approaches), and credit mitigation
techniques. Credit risk is currently the major risk to which banks are exposed, and yet techniques to
model and mitigate credit risk are still in their infancy. Regulators with the new BIS Capital
Adequacy Framework currently under discussion are setting new standards that will give a definitive
competitive advantage to the banks that can achieve sophistication in credit risk assessment and credit
risk management.
Chapter 13 proposes a framework for operational risk control. We describe four key steps in
implementing bank operational risk, and highlight some means of risk reduction. Finally, we look at
how a bank can extract value from enhanced operational risk management by improving its capital
attribution methodologies.
Chapter 14 is devoted to capital allocation and performance measurement. This chapter presents the
Risk Adjusted Return on Capital (RAROC) analysis to measure performance and allocate economic
capital. It provides managers with the information they need to make the trade-off between risk and
reward more efficient.
Chapter 15 elaborates on "model risk," that is, the special risk that arises when an institution uses
mathematical models to value and hedge securities. We discuss some classic examples of what can go
wrong when trading strategies are built on theoretical valuation models.
Chapter 16 is on risk management for nonfinancial corporations. In this chapter we discuss in detail
the pros and cons of modern risk management techniques as applied to nonbank corporations. The
relevant question is not whether corporations should engage in risk management but, rather, how they
can manage risk in a rational way. We also discuss some new accounting standards that have been
introduced to deal with the derivative and hedging activities of corporations.
Chapter 17 presents our views on risk management in the future. In this chapter we look at how risk
management will be induced—and facilitated—by advances in technology, the introduction of more
sophisticated regulatory measures, rapidly accelerating market forces, and an increasingly complex
legal environment.

Page xxiii
Acknowledgments
Our appreciation goes to many friends and colleagues at CIBC, the Hebrew University, and other
institutions for their generous help. Particular thanks go to the members of the Senior Executive
Team (SET) at CIBC, whose insights toward building best practice as well as practical risk
management tools have been invaluable. Parts of the book were presented in conferences, seminars,
regulatory bodies, and internal CIBC round tables around the world and we have greatly benefited
from the comments of numerous participants. Most of all our appreciation goes to our extended
families.
We would like to extend our debt of gratitude to our outstanding editor Robert Jameson for the many
valuable suggestions that substantially shaped the book, and to Catherine Schwent, acquisitions editor
at McGraw-Hill, for her devotion and patience. Our special thanks go to all those that provided
administrative and typing assistance. They have done a wonderful job considering the tough clients
they had to serve. Parts of the book appeared previously in the working paper series of the Global
Analytics group at CIBC and in a variety of journals, books, and specialized risk publications over the
past many years.
MICHEL CROUHY
DAN GALAI
ROBERT MARK

Page 1
Chapter 1—
The Need for Risk Management Systems
1—
Introduction
The international banking system has experienced many significant structural changes over the last 25
years. Major banks have merged, 1 many institutions have become global,2 and banks seem
increasingly likely to pursue mergers and other alliances with insurance companies.3 Although
institutions have grown in size, competition has substantially increased. This is because, over the same
period, regulators have relaxed their rules and have allowed banks to offer new products and to enter
new markets and new business activities.
The Financial Services Act of 1999 will lead to further far-reaching changes in the U.S. financial
system. It will repeal key provisions of the Glass–Steagall Act, passed during the Great Depression,
which prohibits commercial banks from underwriting insurance and most kinds of securities. Most
significantly, brokerage firms, banks, and insurers will be able to merge with each other; this sort of
alliance was prohibited by the Bank Holdings Act of 1956. The proposed reform is intended to allow
bank holding companies to expand their range of financial services and to take advantage of new
financial technologies such as web-based e-commerce.
The new legislation will also put brokerage firms and insurers on a par with banks by allowing them to
enter into the full range of financial activities and compete globally.

Page 2
The expansion of the activities of bank holding companies will incur new market, credit and
operational risks. The consolidations will also precipitate a thorough revision of capital adequacy
requirements, which are currently tailored to the needs of traditional bank holding companies.
This trend toward consolidation complements longer-term changes in industry structure. Over the
past 20 years, many corporations have found it less costly to raise money from the public (by issuing
bonds) than to borrow directly from banks. Banks have found themselves competing more and more
fiercely, reducing their profit margins, and lending in larger sizes, longer maturities, and to customers
of lower credit quality.
Customers, on their part, are demanding more sophisticated and complicated ways to finance their
activities, to hedge their financial risks, and to invest their liquid assets. In some cases, they are
simply looking for ways to reduce their risk exposure. In other instances, they are willing to assume
additional risk, if they are properly compensated for it, in order to enhance the yield of their portfolio.
Banks are, therefore, increasingly engaged in what might be called "risk shifting" activities. These
activities demand better and better expertise and know-how in controlling and pricing the risks that
banks manage in the market.
As the banking industry has evolved, the managerial emphasis has shifted away from considerations
of profit and maturity intermediation (usually measured in terms of the spread between the interest
paid on loans and the cost of funding) toward risk intermediation. Risk intermediation implies a
consideration of both the profits and the risks associated with banking activities. It is no longer
sufficient to charge a high interest rate on a loan; the relevant question is whether the interest charged
compensates the bank appropriately for the risk that it has assumed.
The change in emphasis from simplistic "profit-oriented" management to risk/return management can
also be seen in non-bank corporations. Many major corporations are now engaged in active risk
management. Of course, "risk" was always a major consideration in deciding whether to take
advantage of investment opportunities. However, rejecting projects because they seem to be risky can
lead companies to reject investment opportunities that in

Page 3
fact offer an excellent return. The real problem is how to quantify risk and thus price it appropriately.
In the banking industry, the classic risk is credit risk. Through history, banks have sought to manage
this risk as a key part of their business. However, it was not until 1988 that a formalized universal
approach to credit risk in banks was first set out. Based on the 1988 Bank for International
Settlements (BIS) Accord (Chapter 2), banks were required by their regulators to set aside a flat fixed
percentage of their risk-weighted assets (e.g., 8 percent for corporate loans, 4 percent for uninsured
residential mortgages) as regulatory capital against default. Since 1998, banks have also been required
to hold additional regulatory capital against market risk in their trading books. 4
At some point in the future, banks may incur regulatory capital charges for funding liquidity risk,
regulatory risk, human factor risk, legal risk, and many other sources of risk.5 These diverse risks,
often grouped together under the term "operational risk," are monitored increasingly closely by
banks. They were the cause of various well-publicized financial disasters during the 1990s, such as
the collapse of Barings Bank in 1995 (the bank lacked adequate operational controls). They have also
provoked many expensive court cases, such as the dispute in 1994 between investment bank Bankers
Trust and corporate giant Procter & Gamble—a case that came to typify the risk that derivatives
contracts might not be legally enforceable or might lead to reputational damage.6
Many risks arise from the fact that today's banks are engaged in a range of activities. They trade all
types of cash instruments, as well as derivatives such as swaps, forward contracts, and options—
either for their own account or to facilitate customer transactions. The Federal Reserve Bank
estimates that in 1996, U.S. banks possessed over $37 trillion of off-balance-sheet assets and
liabilities, compared to approximately $1 trillion dollars only 10 years earlier. The multitude and
magnitude of the instruments, and their complexities, make it essential to measure, manage, and
control the risk of banks.
In this chapter, the process leading to the introduction of risk management systems is described. A
major impetus behind the implementation of risk management systems has been the Basle Committee
on Banking Supervision,7 which is an international extension of the regulatory bodies of the major
developed countries.

Page 4
Banks are also beginning to realize that sophisticated risk control tools make for sounder economic
management. This chapter therefore also explores the trend to make risk management an integral part
of the management and control process of financial institutions, rather than simply a tool to satisfy
regulators. We conclude with a discussion of the recent adoption of formal risk management systems
by nonfinancial corporations.
2—
Historical Evolution
Regulation strongly affects the attitude of financial institutions to risk taking, and often dictates how
they accommodate risk. Around the world, the banking industry is regulated in a variety of ways, and
through a multitude of governing bodies, laws, and bylaws. Two related observations can be made:
nowadays there is a world-wide recognition of the need to measure and control risks in global and
local banking activities, and regulation is converging and becoming more consistent across countries.
But before we look at how this is happening, we need to understand some of the historical foundations
of the banking industry.
The crash of 1929 and the economic crisis that followed led to major changes in bank regulation in the
United States. The regulators focused on what is termed today "systemic risk," i.e., the risk of a
collapse of the banking industry at a regional, national, or international level. In particular, regulators
were concerned to prevent the "domino effect": the chance that a failure by one bank might lead to
failure in another, and then another. In a series of acts and laws, the government tried to increase the
stability of the banking system in order to avoid this and other types of economic crisis. At the same
time, the safety of bank deposits was enhanced by the establishment in 1933 of the Federal Deposit
Insurance Corporation (FDIC). A third set of legislation defined the playing field for commercial
banks: crucially, they were barred from dealing in equity and from underwriting securities. The famous
Glass–Steagall Act of 1933 effectively separated commercial banking and investment banking
activities.
The regulation of the banking industry in the United States in the early 1930s reduced the risk in
banking operations but also acted to reduce competition. For example, in 1933 Regulation Q

Page 5
put a ceiling on the interest rate that could be paid on savings accounts. Reserve requirements
encouraged banks to offer current (checking) accounts that did not pay interest.
Furthermore, a combination of the McFadden Act (1927), which prohibited banks from establishing
branches in multiple states ("interstate branching"), and state regulations led to the establishment of
many small banks that specialized in a particular local market. In effect, the regulations helped to
support "natural" regional monopolies in the supply of banking services. 8
The 1956 Bank Holding Company Act, and the amendments to this act from 1970, limited the
nonbanking activities of commercial banks. Again, the motivation was to reduce the risks to which
banks might be exposed. It was felt that if banks expanded their activities into new and risky areas,
they might introduce idiosyncratic risk, or specific risk, that would affect the soundness of the whole
banking system.
Meanwhile, the environment in which banks operated had begun to change. During the period from
World War II to 1951, interest rates had been pegged and were not used as a tool in the monetary
policy of the Federal Reserve. As a result, bank interest rates were stable over an extended period of
time, with only small changes occurring from time to time. From 1951, however, interest rates
became more volatile. The volatility intensified in the 1970s and 1980s as shown in Figure 1.1.
In effect, the governments of developed economies had begun their slow but consistent withdrawal
from their role as insurers, or managers, of certain risks. The prime example of this change is the
foreign currency market. From 1944, with the signing of the Bretton Woods Agreement, international
foreign exchange rates were artificially fixed. Central banks intervened in their foreign currency
markets whenever necessary to maintain stability. Exchange rates were changed only infrequently,
with the permission of the World Bank and the International Monetary Fund (IMF). These bodies
usually required a country that devalued its currency to adopt tough economic measures in order to
ensure the stability of the currency in the future.
The regime of fixed exchange rates broke down from the late 1960s due to global economic forces.
These included a vast expansion of international trading and inflationary pressure in the

Page 6
Figure 1.1
Short-Term Interest Rates, Business Borrowing Prime Rate (Effective Date of Change),
Commercial Paper (Quarterly Averages)
Source: Board of Governors of the Federal Reserve System
major economies. The shift to flexible foreign exchange rates introduced daily (and intraday)
volatility to exchange rates. As the hitherto obscured volatility surfaced in traded foreign
currencies, the financial market began to offer currency traders special tools for insuring
against these "new" risks.
Figure 1.2 depicts the percentage change in the value of the German deutsche mark with regard
to the U.S. dollar. The shift in the levels of volatility is very noticeable in the early 1970s, as
the currency market moved to floating exchange rates. As indicated in the figure, the shift
precipitated a string of novel financial contracts based on the exchange rates of leading
currencies.
The first contracts tended to be various kinds of futures and forwards, though these were soon
followed by foreign currency options. In 1972 the Mercantile Exchange in Chicago (CME)
created the International Monetary Market (IMM), which specialized in

Page 7
Figure 1.2
Month-End German Deutsche Mark/U.S. Dollar Exchange Rates
Source: Smithson et al. (1995)
foreign currency futures and options on futures on the major currencies. In 1982 the Chicago Board Options Exchange
(CBOE) and the Philadelphia Stock Exchange introduced options on spot exchange rates. Banks joined the trend by
offering over-the-counter (OTC) forward contracts and options on exchange rates to their customers.
The increase in inflation and the advent of floating exchange rates soon began to affect interest rates. From the early
1970s, interest rates and bond prices became increasingly volatile. This volatility grew substantially from the early 1980s
onwards, after the Federal Reserve Bank under chairman Paul Volcker decided to use money supply (rather than interest
rates) as a major policy tool. From that point on, interest rates were able to react to changes in the money supply without
prompting interference from the Federal Reserve.
Figure 1.3 charts the volatility of interest rates as measured by percentage changes in the yield of U.S. Treasury bonds
with five

Page 8
Figure 1.3
Percentage Change in Yields on Five-Year U.S. Treasury Bonds
Source: Smithson et al. (1995)
years to maturity. The figure notes the various financial contracts on interest rates or bond prices that have been
introduced since 1975.
As the figure suggests, the market response to the increased interest rate volatility was to create a wide range of new
instruments to trade these risks. New options on Treasury bills, Treasury notes, and long-term government bonds, as well
as futures on synthetic government bonds, were offered by the exchanges; a multitude of over-the-counter (OTC) interest-
sensitive instruments were marketed by banks and other financial intermediaries.
Futures were the first type of instrument to be introduced. The first traded futures on the long-term bonds issued by the
U.S. Government National Mortgage Association (GNMA)—the bonds are backed by mortgage portfolios—appeared in
October 1975 on the Chicago Board of Trade (CBOT). The CME added futures on Treasury bills in early 1976, and on
Eurodollars in 1981. The CBOT

Page 9
introduced futures on Treasury bonds in August 1977, and on Treasury notes in May 1982.
In the second wave of instruments, options on fixed-income securities were introduced. In October
1982, the CBOT started trading options on Treasury bond futures. The Chicago Board Options
Exchange (CBOE) introduced options on Treasury bonds in the same month. The CME introduced
options on Eurodollar futures in March 1985, and on Treasury bill futures in April 1986.
Banks came up with their own form of OTC interest rate derivative—the interest rate swap—in 1982.
In early 1983 they added to their arsenal forward rate agreements (FRAs). Since then commercial
banks and investment banks have introduced a huge number of different types of derivative; the OTC
instruments both compete with exchange-traded derivatives and, in a sense, complement them.
Figure 1.4 depicts the evolution of risk management instruments over a period of 20 years, starting in
1972. Some of the products are exchange-traded, but most are OTC or interbank products.
The huge expansion in derivative product trading around the world spurred the creation of new
specialized exchanges in many countries. In turn, the existence of publicly traded and liquid
derivative contracts helped banks to promote new, more complex, OTC products—and encouraged
additional financial institutions to participate in the new markets.
In April 1995 the Bank for International Settlements, based in Basle, Switzerland, coordinated the
first major survey of derivative markets among 26 central banks of the most developed countries.
The survey, which came to be repeated every quarter, gathered data on the notional amounts of
derivative contracts that were outstanding in each of the participating countries, turnover data, and
market values. Table 1.1 shows the notional amounts and market values of outstanding OTC
derivative contracts, globally and for the United States, at the end of December 1998, compared to
the values at the end of March 1995.
The global market for OTC derivatives amounted in 1995 to over $47 trillion, of which $12 trillion
was booked in the United States. 9 The global market had increased by almost 80 percent and had
reached over $80 trillion by the end of 1998. Interest rate derivatives reached $26 trillion in March
1995, and almost 70 percent

Page 10
Figure 1.4
The Evolution of Risk Management Products
Source: The Economist, April 10, 1993
of this sum took the form of swaps. Volumes almost doubled to $50 trillion by the end of 1998.
Foreign exchange derivatives reached over $13 trillion in 1995, and $18 trillion in 1998, mainly in
forward contracts. (Note that the OTC market for equity derivatives remained relatively small,
especially in the United States.)

Page 11
TABLE 1.1
The Global Over-the-Counter (OTC) Derivative Markets1
Positions at End-December 1998 in Billions of U.S. Dollars
Memorandum Items: Positions at End-March
End-December 1998 19952
National Gross Market Gross Market
Amounts Values National Amounts3 Values3
A. Foreign exchange contracts 18,011 786 13,095 1,048
Outright forwards and forex swaps 12,063 491 8,699 622
Currency swaps 2,253 200 1,957 346
Options 3,695 96 2,379 71
B. Interest rate contracts4 50,015 1,675 26,645 647
FRAs 5,756 15 4,597 18
Swaps 36,262 1,509 18,283 562
Options 7,997 152 3,548 60
C. Equity-linked contracts 1,488 236 579 50
Forwards and swaps 146 44 52 7
Options 1,342 192 527 43
D. Commodity contracts5 415 43 318 28
Gold 182 13 147 10
Other 233 30 171 18
Forwards and swaps 137 — 120 13
Options 97 — 51 5
E. Estimated gaps in reporting 10,371 490 6,893 432
Grand total 80,300 3,230 47,530 2,205
Gross credit exposure6 1,329
Memorandum items:
Exchange-traded contracts7 13,549 10,310
1All figures are adjusted for double-counting. Notional amounts outstanding have been adjusted by halving positions vis-à-vis other reporting dealers.
Gross market values have been calculated as the sum of the total gross positive market value of contracts and the absolute value of the gross negative
market value of contracts with nonreporting counterparties.
2In addition to changes in reporting months, differences in the reporting basis (locational reporting in 1995; worldwide consolidated reporting in 1998)
and in the number of participating countries (26 in 1995; Group of Ten countries in 1998) mean that the two surveys are not really comparable.
3Data for outright forwards and forex swaps are incomplete because they do not include outstanding positions of reporting dealers in the United
Kingdom. Data for total foreign exchange and interest rate contracts include ''other" products that are not shown separately.
4 Single-currency contracts only.
5Adjustments for double-counting at end-June 1998 have been estimated using the results of the 1995 Triennial Central Bank Survey of Foreign
Exchange and Derivatives Market Activity.
6 Gross market values after taking into account legally enforceable bilateral netting agreements.
7 Sources: Futures Industry Association and various futures and options exchanges.
Source: BIS

Page 12
Here we should introduce a note of caution. The "notional value" of a derivative contract is a term
that is used to describe the amount of the underlying price reference (e.g., foreign currency) stipulated
in the derivative contract. This means that the notional value is not always related very strongly to the
economic value of the derivative contract. For example, a deep-out-of-the-money option might have a
high notional value, but a very small or negligible market price (or economic value). Thus,
aggregating derivative notional values—e.g., those for options that are deep out and deep in the
money—can generate some very misleading statistics.
The second and fourth columns of Table 1.1 attempt to get around this problem by offering estimates
of the market value of OTC derivatives. The total global market value of OTC products was, for
March 1995, $2.2 trillion, and $3.23 trillion at the end of 1998. Exchange-traded contracts possessed
a gross market value of $1.33 trillion on December 1998.
In Table 1.2, Part A and Part B show, respectively, the breakdown of the global OTC foreign
exchange and interest rate derivatives market. The survey results for the end of December 1998 are
compared to the survey results six months earlier, but the main point of interest for our purposes is
the different kinds of products that can be seen in each market. In the foreign currency OTC market,
more than 80 percent of the contracts are for terms of shorter than one year. The dominant currency
is the U.S. dollar.
For interest rate products, the majority of the contracts are for terms of between one and five years,
and approximately 20 percent are for terms longer than five years. The dollar is the most prominent
currency, but it accounts for only about one-quarter of the interest rate contracts.
The outstanding notional amount of derivatives is not necessarily correlated with the intensity of
trading. Table 1.3 provides data on the average daily turnover in notional amounts for foreign
currency and interest rate derivatives, comparing the positions on April 1995 to the positions
recorded for April 1998.
Of the $961 billion of daily OTC turnover in foreign currency derivatives in April 1998, $699 billion
was in the form of foreign currency swaps and $106 billion was in the form of forward contracts.
Almost 90 percent of the foreign currency contracts are in U.S. dollars (i.e., U.S. dollars versus other
currencies).

Page 13
TABLE 1.2: Part A
The Global OTC Foreign Exchange Derivatives Markets1
Amounts Outstanding in Billions of U.S. Dollars
End-June 1998 End-December 1998
Gross Gross
Notional Market Notional Market
Amounts Values Amounts Values
Total contracts 18,719 799 18,011 786
with other reporting dealers 7,406 314 7,284 336
with other financial institutions 7,048 299 7,440 297
with nonfinancial customers 4,264 186 3,288 153
up to one year2 16,292 — 15,795 —
between one and five years2 1,832 — 1,624 —
over five years2 595 — 592 —
U.S. dollar 16,167 747 15,810 698
Deutsche mark 4,685 109 4,505 115
Japanese yen 5,579 351 5,319 370
Pound sterling 2,391 55 2,612 62
French franc 1,418 36 1,241 40
Swiss franc 1,104 35 937 30
Italian lira 1,051 24 822 35
Other 5,043 241 4,777 222
Memorandum item:
Exchange-traded contracts 103 — 57 —
1See footnote 1 to Table 1.1. Counting both currency sides of every foreign exchange transaction means that the currency
breakdown sums to 200 percent of the aggregate.
2 See footnote 6 to Table 1.1.
The breakdown of daily turnover of interest rate derivatives between exchange-traded and OTC-traded
shows that $1361 billion were traded on exchanges in April 1998 and only $275 billion in the OTC
markets. The situation is completely different in the case of foreign currency contracts: here most of the
daily trading is in OTC instruments.
It is interesting to note that in this period nonfinancial firms engaged in a daily volume of $168 billion in
foreign currency products, but traded only a volume of $27 billion in interest rate

Page 14
TABLE 1.2: Part B
The Global OTC Interest Rate Derivatives Markets1
Amounts Outstanding in Billions of U.S. Dollars
End-June 1998 End-December 1998
Gross Gross
Notional Market Notional Market
Amounts Values Amounts Values
Total contracts 42,368 1,160 50,015 1,675
with other reporting dealers 18,244 4,63 24,442 748
with other financial institutions 18,694 515 19,790 683
with nonfinancial customers 5,430 182 5,783 244
up to one year2 17,423 — 18,185 —
between one and five years2 16,805 — 21,410 —
over five years2 8,141 — 10,420 —
U.S. dollar 13,214 311 13,762 370
Deutsche mark 6,483 191 9,222 362
Japanese yen 7,164 194 9,763 212
Pound sterling 3,288 58 3,911 130
French franc 3,196 106 3,576 177
Swiss franc 1,055 19 1,320 31
Italian lira 2,082 116 2,130 169
Other 5,887 164 6,331 224
Memorandum item:
Exchange-traded contracts3 13,107 — 12,305 —
1 See footnote 1 to Table 1.1.
2 Residual maturity.
3 See footnote 6 to Table 1.1.
Source: BIS "Central Bank Survey of Foreign Exchange and Derivatives Market Activity, 1998". Basle, May 1999.
products. Undoubtedly, the exposure to foreign currency risk is the key risk factor for many nonbank
corporations.
The various needs of the multinationals explain some of the changes in the banking industry in the 1970s
and 1980s. The rapid changes in global markets and the creation of large multinational corporations, on
the one hand, and technological change in the form of computerized information systems on the other,
offered incentives to merge banks. It was argued that merged banks would

Page 15
TABLE 1.3
Global Turnover in OTC Derivatives Markets
Daily Averages in Billions of U.S. Dollars
Total Foreign Exchange1 Interest Rates2
April 1995 April 1998 April 1995 April 1998 April 1995 April 1998
Total reported gross turnover 1,368 1,990 1,114 1,576 254 415
Adjusting for local double-counting3 –206 –306 –161 –235 –45 –71
Total reported turnover net of local double-counting 1,162 1,684 953 1,341 209 344
("net-gross")
Adjustment for cross-border double-counting3 –323 –457 –265 –380 –58 –78
Total reported "net-net" turnover 839 1,226 688 961 151 265
with reporting dealers 529 764 427 615 102 150
local 207 306 162 235 45 71
cross-border 322 457 265 380 57 78
with other financial institutions 181 267 149 178 32 89
local 90 125 74 80 16 46
cross-border 91 142 75 99 16 44
with nonfinancial customers 129 195 111 168 17 27
local 88 127 76 110 12 16
cross-boarder 41 68 35 58 5 10
Estimated gaps in reporting4 41 39 32 29 9 10
Estimated global turnover 889 1,265 720 990 160 275
Memorandum item:
Exchange-traded products5 1,222 1,373 17 12 1,205 1,361
1 Including outright forwards and foreign exchange swaps.
2 Single-currency contracts only.
3 Made by halving positions vis-à-vis other local reporting dealers and other reporting dealers abroad respectively.
4 Estimates have been prepared for less than full coverage of derivatives market activity in the reporting countries.
5 Sources: Futures Industry Association and various futures and options exchanges.
Source: BIS, "Central Bank Survey of Foreign Exchange and Derivatives Market Activity – 1998," Basle, May 1999.

Page 16
be able to exploit economies of scale, and be better placed to serve the changing needs of their global
clients.
Regulatory bodies also became more willing to allow competition on a global scale: foreign banks
were allowed to operate in local markets, both directly and by acquiring local banks. 10
The trend of mergers and globalization continued through the 1990s among nonbank corporations.
The August 1998 merger of Chrysler of the United States with Daimler-Benz of Germany, and Ford's
expansion into Europe and Japan through the purchase of local manufacturers, illustrates this
continuing trend. Major technological leaders such as Microsoft and IBM are naturally becoming
global giants, but smaller technological companies are also becoming international. This quickening
process of globalization exposes banks and other corporations to ever-greater foreign currency and
interest rate risks.
Currently, banks remain the major players in derivatives trading. Table 1.4 shows the revenues
generated by the top eight commercial banks in the United States, and totals for the other 496
commercial banks dealing in derivatives for the first quarter of 1997. The first column of the table
shows the notional value of derivatives activity, which amounted to over $20 trillion.
It is interesting to note that Chase Manhattan Bank, for example, had income from derivatives of
$121 million in 1992 and $201 million in 1993, compared to $375 million for the first quarter of
1997. For JP Morgan, the numbers for 1992 and 1993 were, respectively, $333 and $797 million,
compared to $590 million for the first quarter of 1997. In notional amounts, JP Morgan expanded its
activity from $1654 billion on December 31, 1993, to $5217 billion on March 31, 1997.
Table 1.5 provides information about the annual growth of derivative products, in terms of notional
and gross replacement value (GRV), for four leading U.S. banks from 1992 to 1996. (Gross
replacement value is simply the sum of the positive replacement values of the instruments that a
bank holds: in other words, the gross market value.)
The numbers emphasize the growing importance of derivatives in banking activities, as well as in the
financial markets. It is interesting to note that the notional amount of derivatives has increased
steadily, while the GRV is not fully correlated to the growth

Page 17
TABLE 1.4
Trading Revenues from Cash Instruments and Off-Balance-Sheet Derivatives, March 31, 1997
Trading Revenues ($ million)
Total Cash and Off-
Notional Value of Interest Rate Foreign Exchange Commodities and Balance-
Derivatives Activity Positions Positions Equity Positions Other Positions Sheet Revenue
Chase Manhattan 6,357,063 168 155 12 41 375
JP Morgan 5,216,959 552 –33 67 3 590
Citibank 2,540,614 219 224 114 0 557
Bankers Trust 1,951,705 149 43 36 25 253
Bank of America 1,672,667 100 48 0 -5 143
NationsBank 1,370,518 37 18 13 13 21
First National Bank of Chicago 1,091,173 -9 14 6 1 72
Republic Nat. Bank of New York 331,346 15 27 -9 10 43
Top eight commercial banks with derivatives 20,532,045 1,231 495 239 88 2,054
Other 496 commercial banks with derivatives 1,335,619 118 195 7 9 329
Total amounts for all 584 banks with derivatives 21,867,664 1,350 690 246 97 2,383
Data are preliminary; revenue figures are for first quarter (not year-to-date).
Currently the report does not include trading revenues from credit derivatives. Credit derivatives have been excluded from the sum of total derivatives here. Trading revenue is defined here as "trading revenue
from cash instruments and off-balance-sheet derivative instruments."
Before first-quarter 1995, total derivatives included spot foreign exchange. Beginning in first-quarter 1995, spot foreign exchange was reported separately.
Numbers may not add up due to rounding. Source: Office of the Comptroller of the Currency.
Source: Risk, August 1997.

Page 18
TABLE 1.5
Notional Amounts of Derivatives of Leading Banks and Their Gross Replacement Value (GRV), 1992–1996, in Billions of U.S. Dollars
19921 19931 19942 19953 19963
Banks Notional GRV4 Notional GRV Notional GRV Notional GRV Notional GRV
Chase Manhattan 841 18.0 925 14.5 1293 14.5 4834 ng5 5712 ng
Chemical 1621 23.0 2479 24.2 3182 18.0
CitiCorp 1539 29.5 1975 23.5 2665 27.5 2376 16.1 2522 17.5
JP Morgan 1278 22.0 1654 30.7 2972 31.1 3447 16.1 4716 62.4
1 Risk 7 (9) Sept. 94, p.93.
2 Risk 8 (10) Oct. 95, p.26.
3 Risk 10 (9) Sept. 97, p.39.
4 GRV = Gross replacement value is the sum of positive replacement value or gross market value.
5 ng = not given.

Page 19
of the notional amount, due mainly to the hedging strategy used by each bank. For example, the
notional amount and the GRV of the JP Morgan derivative book increased by a ratio of 3.69 and
2.82, respectively, over the five-year period.
3—
The Regulatory Environment
So far in this chapter, we have explained how the global environment became riskier as the financial
markets were liberalized, and we have charted the consequent growth in risk management products in
terms of the types of instrument and the volumes traded. Now it is time to turn our attention back to the
regulatory environment.
In 1980 the Depository Institutions Deregulation and Monetary Control Act (DIDMCA) marked a
major change in regulatory philosophy in the United States. This act was an important step in the
deregulation of the banking system, and the liberalization of the economic environment in which banks
operate. The act initiated a six-year phase-out period for Regulation Q, which had placed a ceiling on
the interest rates that banks could offer deposit accounts with check facilities and savings deposits. The
act allowed commercial banks to pay interest on accounts with withdrawal rights (the so-called
"NOW" accounts).
This trend continued with the 1982 Garn–St. Germain Depository Institution Act (DIA), which
allowed banks to offer money market deposit accounts, and the so-called "super-NOW" accounts
(i.e., accounts that paid interest but offered limited check-writing privileges).
These regulatory moves opened up the banking industry to further competition from federally
chartered thrift institutions, but they also allowed commercial banks to expand by buying failed savings
banks. By the late 1970s and early 1980s, the numbers of such failed institutions had increased
substantially. The main reason was an economic squeeze on banks that held sizable fixed-rate loan
portfolios and which had financed these portfolios by means of short-term instruments. The inflationary
environment of the 1970s left such institutions exposed to rising interest rates.
Regulation Q, before it was changed, also helped to drive small depositors away from such banks.
They turned instead to

Page 20
market-traded instruments that offered a better return, such as Treasury bills, certificates of deposit
(CDs are short-term debt instruments issued by banks), and, later, to money market deposit accounts
and NOW accounts.
Many of the banks exposed to the mismatch between short-and long-term funds failed to hedge this
exposure. In part, they were simply not familiar with the risk-shifting mechanism provided by
derivatives, though often their charter acted to prevent them from using such instruments.
Interestingly, the push to implement risk management systems in banks came, primarily, from the
regulators (rather than from inside banking institutions). In the mid-1980s, the Bank of England and the
Federal Reserve Board became concerned about the growing exposure of banks to off-balance-sheet
claims, coupled with problem loans to third-world countries. At the same time, regulators in the United
Kingdom and the United States came under pressure from international banks with headquarters in the
two countries. The banks complained of unfair competition from foreign banks, especially from Japan
and the Far East, that were subject to much more lenient regulations and, especially, that were not
subject to formal capital requirements.
The response of the Bank of England and the Federal Reserve Bank was, first of all, to strengthen the
equity base of commercial banks by requiring that they set aside more capital against risky assets. As
far as capital requirements were concerned, the approach was to demand more capital than before: at
least 8 percent against risk-weighted assets. In addition, the regulators proposed translating each off-
balance-sheet claim into an equivalent on-balance-sheet item, so that capital could be assessed against
derivative positions.
Secondly, the regulators attempted to create a "level playing field." They proposed that all
international banks should adopt the same capital standard and the same procedures. The Federal
Reserve Board and the Bank of England assigned to the BIS the job of studying the positions of banks
worldwide, planning out the details of the proposition, and proposing a set of common procedures to
the regulating bodies.
The BIS continued the process initiated by the Federal Reserve Bank and the Bank of England by
sending drafts of the proposals to the banks and asking for their comments and suggestions. It was
clear at the outset that the task was very complicated and would

Page 21
require a high level of both investment and commitment from all the banks.
It was the explicit intention of the BIS that their interim proposals should be adopted, tested, and later
amended according to any accumulated experience. Thus, the story of bank regulation since the 1980s
has been one of an ongoing dialogue between the BIS and commercial banks all over the world, with
the active involvement of local central banks and local controllers of banks.
The first results of this process, the 1988 BIS Accord and its subsequent amendments, are introduced
in Chapter 2 and described in detail in Chapter 4. As Chapter 2 recounts, while the regulatory bodies
initiated the process and drew up the first set of rules, they have accepted that sophisticated banks
should have a growing role in the setting up of their own internal risk management models. With the
principles set and the course defined, the role of the regulators has begun to shift to that of monitoring
sophisticated banks' internal risk management systems.
Few professionals in the banking industry believe that the systems proposed (or imposed) by the BIS
are, in any sense, perfect. Nevertheless, the role of the BIS in forcing the banks to quantify risks,
evaluate risks, price risks, and monitor risks has proved invaluable. Further, regulators seem
increasingly open to the idea of a two-tier approach. This allows the more sophisticated financial
institutions to make use of their own internal models, while applying a simpler standardized approach
to the majority of institutions.
There have also been important industry initiatives over the last 10 years. The Group of Thirty (G-30)
study published in July 1993 was the first industry-led and comprehensive effort to broaden awareness
of advanced approaches to risk management. The G-30 study provides practical guidance in the form
of 20 recommendations, addressed to dealers and end-users alike, in terms of managing derivatives
activities. We discuss these recommendations in more detail in Chapter 2.
4—
The Academic Background and Technological Changes
Risk management cannot be understood independently of the body of academic research published
on risk management techniques

Page 22
and derivative valuation that has evolved since the early 1950s. A common deficiency in risk
management systems and policy proposals is the lack of a firm theoretical foundation (and therefore
consistency).
In this section we review some of the key theories and models, and show how they relate to the
development of approaches to risk management in banking. However, it is worth making clear at the
outset that the theoretical work on risk management is based on many simplifying assumptions, and
that the implementation of theoretical work is not always straightforward. Real life is complicated and
is composed of many details that models cannot, and maybe should not, accommodate. Instead, the
role of models is often to simplify complicated structures and to highlight the most important factors.
A ''good" financial model is one that helps the analyst separate out the major explanatory variables
from a noisy background.
Milton Friedman, in his seminal article "The Methodology of Positive Economics" (1953),
emphasizes that a model can be only evaluated in terms of its predictive power. It cannot be evaluated
in terms of the assumptions employed, or in terms of whether the model seems to be sufficiently
complicated to capture all the relevant details from "real life." In other words, a model can be simple,
and yet be judged successful if it helps in predicting the future and in improving the efficiency of the
decision-making process.
The word "risk" has many meanings and connotations. It is widely used by professional traders, risk
managers, and the public. Many articles in newspapers and magazines talk about risky and choppy
markets. They warn their readers from investing "too much" in "risky assets," and they wonder
whether financial markets have become "too risky" and volatile. A proliferation of names has
emerged to describe the various risks: business risk, financial risk, market risk, liquidity risk, default
risk, systematic risk, specific risk, residual risk, credit risk, counterparty risk, operations risk,
settlement risk, country risk, portfolio risk, systemic risk, legal risk, reputational risk, and more.
The foundations of modern risk analysis are contained in Markowitz's (1952) paper concerning the
principles of portfolio selection. Markowitz showed that a rational investor, i.e., an investor who
behaves in a way that is consistent with Von Neuman–Morgenstern's expected utility maximization,
should analyze

Page 23
alternative portfolios based on their mean and on the variance of their rates of return.
Markowitz makes two additional assumptions: first, that capital markets are perfect, 11 and
second that the rates of return are normally distributed.
Since the utility choices of a consumer can be expressed in terms of two parameters
only—mean and variance—portfolios of investments can also be presented for selection
according to these two parameters.
Note that the two-parameter presentation, while valid for well-diversified portfolios, does not
apply to individual securities. A security should be evaluated only in the context of the
portfolio of investments to which it belongs, through its contribution to the mean and variance
of the portfolio. More specifically, the risk of a single investment should be measured in terms
of the covariability12 of its rate of return with the rate of return of the portfolio.13
Markowitz's portfolio analysis suggests that the specific or idiosyncratic risk of a single
security (i.e., the elements of its risk profile that it does not share with other investments)
should not be measured in terms of its volatility as measured by the variance of the rates of
return. The variance measures the potential dispersion of future rates of return, but this is not a
relevant risk measure for a single security. This is because most of the specific risk due to
volatile returns can easily be diversified away and eliminated at virtually no cost. It follows
that the specific risk, or idiosyncratic risk, of a security, should not be priced in the
marketplace if it can easily be offset against the returns of other securities.
Sharpe (1964) and Lintner (1965) take the portfolio approach one step further by adding the
assumption that a risk-free asset exists. They show that financial markets are in equilibrium
when all investors hold a combination of a riskless asset and the market portfolio of all risky
assets in the economy. Therefore, prices of risky assets are determined in such a way that they
are included in the market portfolio. They show that in order to be "in" the market portfolio, a
risky asset must be priced according to its relative contribution to the total risk of the market
portfolio, as measured by the variance of its rate of return distribution, :

Page 24
where Ri and RM are the rates of return on asset i and the market portfolio, respectively, σi and
σM are the standard deviations of the rates of return on asset i and the market portfolio,
respectively, and ρi,M is the correlation coefficient between i and M.
This ratio is called the "beta" of asset i (βi). It measures the systematic risk of the asset, i.e., the
risk that cannot be diversified away. 14
The relative contribution is measured by the ratio between the covariance of the rate of return
of the asset, and the rate of return of the market portfolio, and the variance of the market
portfolio. It should be noted that the weighted sum of all the covariances is equal to , the
total risk of the market portfolio:
Here, xi denotes the relative weight of security i in the market portfolio, N is the number of
assets in the market portfolio, and . The previous expression can be rewritten as:
The beta risk measures the relative comovements of security i for which investors should be
compensated.
Sharpe (1964) and Lintner (1965) proved that the expected rate of return on security i under the
above assumptions, is given by the following equation:
where E(·) is the expected value operator, and R denotes the rate of return on the riskless bond
over the same holding period as the asset. The term in brackets measures the risk premium in
the market for a unit of beta risk. The product of βi and (E(RM) – R] is the expected
compensation that holders of asset i require above the risk-free rate R in order to hold the asset.
If we rewrite the equation above in terms of σi, σM, and ρi,M, then E(Ri) = R + σi ρi,M [E(RM) –
R]/σM. Accordingly, the excess expected return above the risk-free rate is a function of the
systematic component of risk σi ρi,M times the unit price of risk [E(RM) – R]/σM.

Page 25
Concurrently, most investment banks and brokerage firms calculate the beta of individual
securities as well as their volatility, or total risk as measured by σi. The beta is estimated from
the regression equation,
where Rit and RMt are the rates of return measured between time t and t-1 for security i and an
index representing the "market portfolio of risky assets," respectively. R is the short-term
riskless interest rate, εit is the residual value, and ai and bi are the two regression parameters,
with bi being the statistical estimate of βi.
The original model, known as the "Capital Asset Pricing Model" (CAPM), was proved and
tested in discrete time, for example, over a one-year or one-month horizon. Merton (1972) has
shown that the CAPM can also be derived in a continuous time framework, under the
assumptions that trades can be executed at any time and that the return-generating process for
stock prices is smooth, with no jumps in prices (i.e., it behaves like a diffusion process).
The next important development in the analysis of risk occurred in 1973, with the publication
of two seminal papers by Fischer Black and Myron Scholes, and Robert Merton, on the pricing
of options. The papers make use of a framework similar to that used by Markowitz, Sharpe,
and Lintner; namely, they assume the existence of perfect capital markets and assume that
security prices are lognormally distributed or equivalently, that log-returns are normally
distributed. To these, they add the new assumptions that trading in all securities is continuous
and that the distribution of the rates of return is stationary. The Black–Scholes (BS) option
pricing model (OPM) for European call options on stocks (without dividends) is given by:
where C is the premium of a European call option, S is the price of the underlying security, K
is the exercise or strike price, r is the riskless instantaneous interest rate, 15 τ is the time period
to the maturity of the option, N(·) is the cumulative standard normal distribution, and where

Page 26
Here, σ is the standard deviation of the rate of return distribution of the underlying security, ln is the
natural logarithm operator, and e is the exponent operation (e = 2.714 . . .).
For example, a one-year (τ = 1) at-the-money (K = S) call on a stock with current price of $100 (S =
$100) and standard deviation of 20 percent (σ = 0.20), when the annual interest rate is 10 percent, is
valued at $13 according to the Black–Scholes model.
The pricing model for a European put option can easily be derived from the call value by using what
has become known as the "put-call parity relationship": 16
where P is the premium on a European put. The BS model for a European put is therefore:
Continuing our numerical example, the price of an at-the-money put should be $3.90.
The risk of the underlying security, which determines the premium on the option and its risk, is
measured by its volatility σ. An increase in the volatility of the underlying stock, with all other
parameters unchanged, causes an increase in the option's premium. It can be shown that the
instantaneous volatility of the option is given by:
where σi and ηi,s are, respectively, the instantaneous standard deviation of derivative i and the
elasticity of the derivative i with respect to the underlying asset, S, and subscript c stands for a call
and p for a put. For a call option, the elasticity is
and for a put

Page 27
Continuing with our example, since N (d1) = 0.72 and –N (–d1) = – 0.28, therefore ηc,s = 5.53
and ηp,s = –7.23. Accordingly, τc = 5.53 · 0.20 = 1.11 (or 110 percent) and σp = 7.23 · 0.20 =
1.45 (or 145 percent).
In a similar way the systematic risk of a call (βc) and a put (βp) is given by:
where β is the systematic risk of the underlying asset.
If we assume that the underlying asset has a beta of 1, then the instantaneous beta of the call is
5.53, and –7.23 for the put. By adding the put to the portfolio of securities with positive beta
risk, the systematic risk of the portfolio is reduced; conversely, adding calls increases the beta
of the portfolio.
Note that N(d1) and –N (–d1) are the hedge ratios, known also as the "delta" of the option, of a
call and of a put, respectively. The hedge ratio measures the change in the value of an option
resulting from a small change, say a dollar, in the price of the underlying security. The hedge
ratio shows how the risk of the underlying security over a very short time interval can be
hedged dynamically with derivatives assets. A fully hedged position over an arbitrarily small
interval of time is often called a "delta-neutral" position.
In order to complete this brief introduction to the theoretical basis of modern risk management,
we must turn to the work Franco Modigliani and Merton Miller published in 1958. 17 These
academics showed that in a perfect capital market, with no corporate and income taxes, the
capital structure of a firm has no effect on the value of the firm. A corporation cannot increase
its value by issuing more debt, despite the fact that the expected cost of debt is lower than the
expected cost of equity. Instead, the greater leverage in the capital structure in the firm,
brought about by the increased level of indebtedness, means that the equity holders
immediately face a greater level of financial risk. Naturally, they will demand compensation
for this in the form of higher rates of return.
This implies that management should concentrate on identifying and implementing
investments that will increase the economic value of the firm, rather than reengineering the
capital

Page 28
structure of the firm. The cost of capital of the firm, which is equal to the weighted cost of equity and
debts, is important mainly in the sense that it offers a marginal "hurdle rate" for management in their
evaluation of new investments.
Many of the contributors to the intellectual framework that we have just sketched out were eventually
awarded the Nobel Prize. Their fundamental results will accompany us throughout this book,
providing an essential framework for risk analysis and evaluation. In Chapter 9 we present an
integrated approach that combines the Black–Scholes option pricing model with the CAPM in the
Modigliani–Miller framework, in order to evaluate credit risk and default risk.
Furthermore, in order to understand the BIS recommendations concerning capital adequacy in the
banking industry, one has to understand Markowitz's approach to risk and reward; the importance of
measuring the correlation coefficients among different bank assets and liabilities is directly linked to
the portfolio diversification effects of the fundamental model.
Readers unfamiliar with the work of Markowitz, Sharpe, Lintner, Modigliani and Miller, or indeed
Black and Scholes, may wish to study one of the standard text books devoted to these theoretical
advances as they read further into this present book. 18
Of course, developing fundamental theories on risk management and implementing those theories
within a business are two very different challenges. There are two prerequisites for any risk
management system: first, reliable, broad, and up-to-date databases concerning both the bank's
transactional positions and the financial rates available in the wider marketplace; and second,
statistical tools and procedures that allow the bank to analyze the data.
Global banks and corporations are engaged in many transactions each day, and may carry millions of
open positions in their books. All these positions have to be evaluated periodically, usually on a daily
basis for international banks, to assess the net risk exposure of the bank. This often means a bank
must bring together data from a multiplicity of legacy systems with different data structures, from all
of its branches and businesses worldwide—as we discuss in later chapters. The data collected must be
as accurate as possible, while minimizing omissions. In addition, market

Page 29
data history for interest rates, foreign exchange rates, commodities, equities, and other associated
derivatives must be collected and analyzed in order to estimate volatilities and correlations of major
risk factors. The results of these analyses form key inputs into the pricing models used to assess the
risks inherent in the various financial claims. Measuring risk is thus based on statistical procedures.
The major tools used by financial analysts in this regard are often based on research by academics
seeking to improve statistical estimation procedures. For example, in the last decade, in reaction to
evidence that volatility in financial markets may be nonstationary, researchers have begun to make use
of increasingly sophisticated procedures such as ARCH, GARCH, and other extensions. 19
5—
Accounting Systems versus Risk Management Systems
So far in this chapter we have looked at risk as it has developed in the financial markets, and at how
banks have sought to analyze this risk. In this section, we take a look at how risk affects financial
reporting.
The traditional accounting approach is, in essence, backward looking. Past profits (or losses) are
calculated and analyzed, but future uncertainties are not measured at all. This was not entirely
satisfactory even when banks derived their profits primarily from two major sources: providing loans
and providing intermediation services.
As we recounted above, however, since the 1980s the growing importance of OTC products has
added a third source of profitability. As the Generally Accepted Accounting Principles (GAAP) could
not easily accommodate derivatives, the instruments have largely appeared in the footnotes to the bank
balance sheet; i.e., they have largely remained an off-balance-sheet activity.
In the major banks, however, this has meant that the size of off-balance-sheet claims, as measured in
notional amounts, have grown to be larger than those that are recorded on-the-balance sheet. The
same sort of accounting problems affect nonbank corporations that engage in derivatives trading.

Page 30
The end result is that a major component of bank profitability over the last decade does not appear in
any consistent way in the financial reports of banks. Shareholders and financial analysts find it
difficult to assess bank performance, while regulators and rating agencies face problems when they
try to determine the riskiness of bank activities. Likewise, the true risk profile of some nonbank
corporations may also be unclear from their financial reports. 20
A thought-provoking illustration of this problem in bank accounting is provided in Table 1.6, which
appeared in The Wall Street Journal (19–20 June 1998). The table shows the problem loans of
Japanese banks as of March 31, 1998, under conventional accounting practices in Japan, as compared
to the new proposed measurement standard. For the largest nine banks in Japan, the average
difference between the reported figures and the figures that would be produced by the proposed
standard is 42 percent (ranging between 29 and 62 percent).
Ideally, the financial world would create a new reporting system based on what might be called
"Generally Accepted Risk Principles" (GARP). The system would be forward looking, and
TABLE 1.6
Measuring Problem Loans for Japanese Banks Under The Old and New System of Reporting, March 31, 1998, in Billions
of Yen
Bank Old New % Change
Dai-Ichi Kangyo Bank 1,185 1,471 24
Sumitomo Bank 1,005 1,469 46
Fuji Bank 1,218 1,629 39
Sakura Bank 1,140 1,475 29
Sanwa Bank 873 1,288 47
Bank of Tokyo Mitsubishi 1,389 2,250 62
Daiwa Bank 673 958 42
Tokai Bank 866 1,222 41
Asahi Bank 704 995 41
Total 9,053 12,757 41
Source: Goldman Sachs

Page 31
designed to help managers and regulators analyze and understand the operations of financial institutions.
The system would also be two-dimensional: the added dimension would be risk, or uncertainty,
concerning future profitability (i.e., potential losses) from different banking activities.
Any such risk-sensitive accounting system would have to compromise between accuracy and
sophistication, on the one hand, and applicability and aggregation on the other. Major problems arise
in any aggregating system when it is applied to factors that are nonlinear, and therefore "nonadditive."
For example, systematic risk (or beta risk) is additive over securities for any given portfolio, but
specific risk, measured by the standard derivation of the residual return, is nonadditive. In other
words, the standard deviation of a portfolio is not the sum of the standard deviations of the securities in
the portfolio. This is why a careful aggregation of risk demands the estimation of many parameters, and
especially the degree of correlation between all the possible pairs of securities in a portfolio.
This has not proved an easy lesson to learn in the banking industry. In 1986, when the Federal
Reserve in the United States and the Bank of England started to create a new system for banks in
Western economies in order to assess capital required to cover the banks' risks, the starting point for
the study was the existing accounting system. The idea was simply to translate off-balance-sheet claims
into their on-balance-sheet equivalents. After the investment of considerable effort, this simplistic
approach was abandoned in favor of the much more comprehensive solution that we outlined above.
It was realized that simply translating each off-balance-sheet claim to its on-balance-sheet equivalent,
and then adding up these individual claims, would hugely overstate the real position and impose a
significant cost on banks. (Chapter 2 introduces the initial minimum required regulatory capital
procedures suggested by the BIS, and Chapter 4 provides details of the procedures of BIS 1998.)
6—
Lessons from Recent Financial Disasters
Since modern banks began to evolve in the seventeenth century, most bank failures have been due to
exposure to bad debts.

Page 32
However, some spectacular bank failures over the last 25 years have been due in part to market
exposures generated by derivative positions—and politicians and the media have suggested
that this is because the banking system as a whole is failing to control these new forms of risk.
It is true that for many years, banks concentrated their efforts on assessing credit risk. Rating
agencies, such as Moody's and Standard and Poor's, were employed to evaluate (or confirm)
the credit quality of large firms that applied for a loan (see Chapter 7). Internal procedures
were also developed in major banks, though they were often lacking, or inadequate, in smaller
institutions. The key weakness in this traditional risk analysis, however, was that credit risk
was evaluated on a case-by-case basis. Correlation risk, i.e., the risk associated with cross-
dependencies among loans, such as the concentration of loans in a certain geographical
location or in a given industry, was often ignored. As a result, American commercial banks
suffered large losses to Latin American counterparties in the 1980s as a result of the economic
crisis in that continent—losses that eventually led to the collapse of Continental Bank in
Chicago. Concentration by business sector can also be catastrophic: Crédit Lyonnais suffered
huge losses from clients engaged in the real estate business in France when this sector entered
into a slowdown in 1992.
Credit correlations are one source of risk, but it has become increasingly clear that
concentrations among different kinds of risks are also crucial. Perhaps the most striking case of
correlation risk across market risk and credit risk is the crisis of the savings and loan industry
in the United States in the 1980s. We have already mentioned in this chapter how these
institutions, locked into long-term fixed-interest loans, were surprised by rising interest rates
on short-term deposits; a crucial additional factor was that many of the loans they had extended
were used to purchase real estate. Unfortunately, but predictably, the value of this real estate
was negatively correlated to the level of interest rates.
It is only in the late 1990s that the banking industry has begun to appreciate the risks of
correlations between credit and market risk, on the one hand, and liquidity risk on the other.
The near-collapse of Long-Term Capital Management (LTCM) in 1998 highlighted the risks of
high leverage to an individual

Page 33
institution. But it also showed how problems in one institution might spill over into the entire financial
system when, simultaneously, market prices fall and market liquidity dries up—making it almost
impossible for wounded institutions to unwind their positions in order to satisfy margin calls. 21
LTCM discovered too late how negatively correlated its returns were with liquidity risk (see Chapter
15 for a more detailed discussion of liquidity risk and the LTCM case). The industry as a whole is
now looking at how the relationship between liquidity risk, leverage risk, and market and credit risk
can be incorporated in risk measurement and stress testing models.
It remains uncertain as to whether risk management can prevent all kinds of major crises. Will the risk
management system really send advance warning signals? Will capital requirements really reduce the
risk of bankruptcy? If not, will they at least diminish the spillover risk or the ''domino effect" risk?22
As Chapters 5 and 8 describe, innovations by the banking industry, such as the development and
publication by JP Morgan of its RiskMetrics and CreditMetrics systems to address market risk and
credit risk, are significant advances in risk management methodology. Yet they do not offer a panacea
to the problem of substantial changes in default rates, interest rates, exchange rates, and other key
indexes over a short time period, say, a day, a week or a month. Increasingly, banks recognize they
must subject their positions to "stress analysis" to measure their vulnerability to unlikely (but possible)
market scenarios (see Chapters 6 and 11).
If "correlation risk" can be identified as one principal source of hidden bank risk, then operational
risks are surely the second major source. The downfall of Barings in February 1995 is often depicted
as the result of the actions of a single trader, Nicholas Leeson, who exposed the bank to huge futures
positions (betting mainly on an increase in the value of the Nikkei 225 index). As the investigation into
the disaster revealed, the bank's collapse also bore witness to the failings of senior managers. Put
simply, they lacked the ability to monitor effectively Leeson's trading activities.
This was partly due to a lack of proper risk management systems, but it was also due to a disregard for
risk management procedures. In particular, Leeson had been placed in charge of trading at the
Singapore branch of Barings Bank while at the same time

Page 34
taking charge of the back-office operation. Yet it is a first principle of risk control that the assessment
of risk, and control over tracking transactions, must be independent of the trading function.
One additional lesson of the Barings debacle is that bank management must scrutinize success stories in
order to evaluate the risks incurred. This is also the lesson from the crisis in Orange County, California,
in 1994. The treasurer of the County borrowed heavily and invested in mortgage-backed securities,
only to incur losses of over $1.6 billion when the cost of borrowing rose. In both the Orange County
and Barings Bank cases, the man in charge showed excellent results at first, and was therefore allowed
to continue to transact without proper surveillance or controls. Managers must remember the cardinal
rule of all investments: reward does not come without risk. (The management of operational risk is
discussed in more detail in Chapter 13.)
7—
Typology of Risk Exposures
In Section 4 we summarized the theoretical framework of risk under the assumption that all assets are
traded in perfect capital markets. In this section, we present a typology of risk exposures from the
point of view of the bank's management, taking into consideration practical issues including the
limitations of models and theories, human factors, existence of "frictions" such as taxes and transaction
cost, and limitations on the quality and quantity of information, as well as the cost of acquiring this
information, and more.
Financial risks can be divided into market risk, credit risk, liquidity risk, operational risk, legal and
regulatory risk, and human factor risk (Figure 1.5).
Market risk is the risk that changes in financial market prices and rates will reduce the value of the
bank's positions. Market risk for a fund is often measured relative to a benchmark index or portfolio,
and is referred to as the "risk of tracking error." Market risk also includes "basis risk," a term used in
the risk management industry to describe the chance of a breakdown in the relationship between the
price of a product, on the one hand, and the price of the instrument used to hedge that price exposure
on the other. The

Page 35
Figure 1.5
Typology of Risks Faced by a Financial Institution
market-VaR methodology, discussed in Chapter 5, attempts to capture multiple components of market
risk such as directional risk, convexity risk, volatility risk, basis risk, etc.
Credit risk is the risk that a change in the credit quality of a counterparty will affect the value of a
bank's position. Default, whereby a counterparty is unwilling or unable to fulfill its contractual
obligations, is the extreme case; however, banks are also exposed to the risk that the counterparty
might be downgraded by a rating agency.
Credit risk is only an issue when the position is an asset, i.e., when it exhibits a positive replacement
value. In that instance, if the counterparty defaults, the bank either loses all of the market value of the
position or, more commonly, the part of the value that it cannot recover following the credit event.
(The value it is likely to recover is called the "recovery value"; the amount it is expected to lose is
called the "loss given default.")
Unlike coupon bonds or loans, the potential loss given default on derivative positions is usually much
lower than the nominal amount of the deal, and in many cases is only a fraction of this amount. This
is because the economic value of a derivative instrument is related to its replacement or market value
rather than its

Page 36
nominal or face value. However, the credit exposures induced by the replacement values of derivative
instruments are dynamic: they can be negative at one point in time, and yet become positive at a later
point in time after market conditions have changed. Therefore, banks must examine not only the
current exposure, measured by the current replacement value, but also the profile of future exposures
up to the termination of the deal.
Chapter 7 discusses the traditional external and internal systems that banks adopt to measure and
manage credit ratings. Chapters 8, 9, 10, and 11 review the new models that have recently become
available to measure credit risk. Chapter 12 reviews the different approaches that banks can employ
to mitigate credit risk.
Liquidity risk comprises both "funding liquidity risk" and "trading-related liquidity risk," though
these two dimensions of liquidity risk are closely related. Funding liquidity risk relates to a financial
institution's ability to raise the necessary cash to roll over its debt, to meet the cash, margin, and
collateral requirements of counterparties, and (in the case of funds) to satisfy capital withdrawals.
Trading-related liquidity risk, often simply called liquidity risk, is the risk that an institution will not
be able to execute a transaction at the prevailing market price because there is, temporarily, no
appetite for the deal on the "other side" of the market. If the transaction cannot be postponed, its
execution may lead to substantial loss on the position. This risk is generally very hard to quantify. (In
current implementations of the market-VaR approach, liquidity risk is included only in the sense that
one of the parameters of a VaR model is the period of time, or "holding period," thought necessary to
liquidate the relevant positions.) Trading-related liquidity risk may reduce an institution's ability to
manage and hedge market risk as well as its capacity to satisfy any shortfall on the funding side
through asset liquidation.
Funding liquidity risk is affected by various factors such as the maturity of liabilities, the extent of
reliance on secured sources of funding, the terms of financing, and the breadth of funding sources,
including the ability to access public markets such as the commercial paper market. It is also
influenced by counterparty arrangements, including collateral trigger clauses, the existence of capital
withdrawal rights, and the existence of lines of credit that the bank cannot cancel.

Page 37
Funding can be achieved through cash and cash equivalents, "buying power," and available credit
lines. (Buying power refers to the amount a trading counterparty can borrow against assets under
stressed market conditions.) In Chapter 15 we discuss in detail the liquidity aspects of the LTCM
crisis mentioned above; in Chapter 6 we present a multiperiod model to incorporate liquidity risk in
scenario analysis and in the VaR framework.
Operational risk refers to potential losses resulting from inadequate systems, management failure,
faulty controls, fraud, and human errors. As we discussed above, many of the recent large losses
related to derivatives are the direct consequence of operational failures. Derivatives trading is more
prone to operational risk than cash transactions because derivatives are, by their nature, leveraged
transactions. This means that a trader can make very large commitments on behalf of the bank, and
generate huge exposures into the future (even up to 30 years ahead), using only a small amount of
cash (at the time that the transaction is executed). Very tight controls are an absolute necessity if a
bank is to avoid large losses.
Operational risk includes "fraud," for example when a trader or other employee intentionally falsifies
and misrepresents the risks incurred in a transaction. Technology risk, and principally computer
systems risk, also falls into the operational risk category. In Chapter 13, we explore some new
approaches to the management of operational risk.
The valuation of complex derivatives also creates considerable operational risk. This risk, generally
referred to as "model risk," is discussed in detail in Chapter 15.
Legal risk arises for a whole variety of reasons. For example, a counterparty might lack the legal or
regulatory authority to engage in a transaction. Legal risks usually only become apparent when a
counterparty, or an investor, loses money on a transaction and decides to sue the bank to avoid
meeting its obligations. 23 Another aspect of regulatory risk is the potential impact of a change in tax
law on the market value of a position. For example, when the British Government changed the tax
code to remove a particular tax benefit during the summer of 1997, one major investment bank
suffered huge losses.
Human factor risk is really a special form of operational risk. It relates to the losses that may result
from human errors such as

Page 38
Figure 1.6
The Dimensions of Market Risk
pushing the wrong button on a computer, inadvertently destroying a file, or entering the wrong value
for the parameter input of a model.
These financial risks can be further decomposed into more specific categories. For example, market
risk could be subdivided into equity risk, interest rate risk, currency risk, and commodity risk (Figure
1.6). Interest rate risk might be further divided into trading risk and gap risk: the latter relates to the
different risk characteristics of bonds based on their maturities. As we discussed earlier, liquidity risk
can be decomposed into two interrelated dimensions: funding liquidity risk and trading-related
liquidity risk (Figure 1.7).
We can slice and dice each risk type down to the most detailed level (Figure 1.8). The more detailed
the decomposition, the more
Figure 1.7
The Dimensions of Liquidity Risk

Page 39
Figure 1.8
Schematic Presentation, by Categories, of the Risk Exposure of a Bank
closely the bank's risk will be captured. In practice, this process is limited by the level of model
complexity that can be handled by the available technology and by the cost and availability of
internal and market data.
8—
Extending Risk Management Systems to Nonfinancial Corporations
Risk management techniques first developed by, and for, banks are now being adopted by firms such
as insurance companies, hedge funds, and industrial corporations. Indeed, there is mounting pressure
from regulators such as the SEC (Securities and Exchange Commission) in the United States, and
from shareholders, for more and better disclosure of financial risk exposures.
The main purpose of risk management systems for nonfinancial institutions is to identify the market
risk factors that affect the volatility of their earnings, and to measure the combined effect of these
factors. The risk issues faced by corporations are different from those faced by financial institutions.
They generally need to look at risk over a longer time, and they must look at how to combine the
effects of their underlying business exposures with

Page 40
those of any financial hedges that they have put in place. The effects of risk on planning and budgeting
must be considered, as opposed to the trader's need to consider profit and loss.
Of course, in a sense nonfinancial corporations have always engaged in activities intended to reduce or
control their risks. For example, they sign long-term contracts with suppliers or clients to reduce
demand and supply uncertainty; they hold inventories and purchase insurance. However, while firms
are already engaged in such risk management activities, they often do not possess a formal system to
monitor general corporate risks and to evaluate the impact of their various attempts to reduce risks.
Meanwhile, academic research has tended to treat each of these areas separately. There are theories
and models to optimize the level of inventories, and there are models to optimize financial hedging
activities (e.g., against exposure to foreign currency risks). There is little in the way of a unified
approach to corporate risk management.
Corporations are often exposed to interest rate risk. For example, they might borrow money from
their bank or provide credit to their customers. They may also be exposed to foreign currency risk if
they export their products or services, or if they depend on supplies from abroad. Most firms have to
account for potential losses that might arise from any default by their clients on receivables, and they
may also incur credit risk if they purchase corporate bonds, or if they engage in OTC derivative
trading. Nevertheless, the risk exposures of nonbank corporations are generally not regulated with the
intensity seen in the risk-related regulation of banks and other financial institutions.
Essentially, this is because the main risk of nonfinancial institutions is business risk, while market risks
and credit risks are secondary in importance. The "domino effect" that is the major worry of bank
regulators is not a major concern in the nonfinancial sector. Nonfinancial corporations are also not as
heavily leveraged as financial corporations. The ratio of debt to total assets in the United States for
nonfinancial corporations is around 30 percent, and in Japan it is approximately 50 percent. For banks,
the ratio is 82 to 92 percent. Finally, the leverage of nonfinancial institutions is primarily of concern to
the firm's creditors, which are usually banks and financial institutions, and not to the general public and
smaller savers.

Page 41
There is one reason, however, why it is now important for nonfinancial corporations to reexamine their
attitudes to risk management. Ironically, this is the huge expansion in derivatives trading itself. In Table
1.3, we can see that nonfinancial firms have increased their daily average turnover in OTC derivatives
(foreign currency and interest rate contracts) from $129 billion in April 1995 to $195 billion in April
1999. While nonfinancial corporations have increased their use of derivatives mainly with the aim of
reducing their financial risk, their involvement in the market means that they must adopt some of the risk
control measures devised by the banking community.
Since current accounting procedures are inadequate for controlling and managing risks, new
procedures must be devised. SEC requirements in effect since 1998 have set new rules for the
disclosure of the market risk exposures of traded companies. In addition, a quantifiable measure of
the exposure to market risk and how it may affect the firm's value or profitability must be supplied.
The trend in many countries is to demand greater transparency with regard to risk management policies
and strategies. Boards of directors will be required to take a more active role in managing risks, and
they will be expected to evaluate returns within the context of the risk. We discuss many of these
themes in more detail in Chapter 16, which is devoted to risk management by nonbank corporations.
Nevertheless, the reader should keep in mind that many of the concepts introduced in other chapters
of this book are also applicable to the risk management efforts of nonfinancial corporations.
Notes
1. For example, in 1993 the old Chase Manhattan Bank and Chemical Bank merged into the new
Chase Manhattan Bank.
2. For example, HongKong and Shanghai Banking Corporation (HSBC).
3. For example, Citicorp, correctly anticipating the new law (Financial Services Act of 1999), has
already merged with insurer Travelers to form the giant one-stop financial conglomerate Citigroup. This
built on an earlier merger (1997), when Travelers, a major insurance and consumer finance concern,
and the U.S. brokerage firm Smith-Barney, merged with the U.S. investment bank Salomon Brothers.

Page 42
4. Chapters 2 and 4 discuss in great detail regulatory capital under both the 1988 and 1998 Accords,
as well as the new BIS proposal for reform of the 1988 Accord.
5. Chapter 13 deals with the management of operational risk, and Chapter 15 discusses different
facets of model risk.
6. Procter & Gamble lost $157 million on two interest swaps that it had entered into with Bankers
Trust, and then sued Bankers Trust for misrepresentation of the risks involved in the transactions. For
details of these financial disasters, see, e.g., Steinherr (1998). Over a nine-day period in April 1994,
Procter & Gamble, Gibson Greetings, and Mead Corporation announced hefty losses from leveraged
swap agreements with Bankers Trust. All three companies filed suits against Bankers Trust.
7. The Basle Committee meets at the Bank for International Settlements (BIS), located in Basle,
Switzerland.
8. In the mid-1980s, there were over 14,000 commercial banks in the United States and 5000 savings
and loan and mutual savings banks.
9. For comparison, the outstanding worldwide securities market debt was $24.4 trillion at the end of
1994 (BIS, 65th Annual Report, 1995) and the outstanding U.S. credit market debt was $17.3 trillion
at the end of March 1995 (Federal Reserve Bulletin, Oct. 1995).
10. HongKong and Shanghai Bank, for example, was allowed to purchase Marine Midland Bank in
the United States and Midland Bank in the United Kingdom.
11. By perfect capital markets, we mean markets with no transaction costs or taxes, where all traders
have free and costless access to all available information and are perfect competitors.
12. The weighted sum of all the covariances is equal to the variance of the portfolio, where the
weights are the same as those used in constructing the portfolio.
13. To illustrate, let us assume that the firm expects to receive an income stream of $15, –$15, and
$15 at the end of years 1, 2, and 3 respectively. The average net income over the three years is $5.
Assume that, as managers of the firm, we have the chance to invest in a project with zero average
value, with net income of –$5 at the end of the year and $5 the year after. If we add this project to the
firm, the expected average profit will remain unchanged at $5. However, the income stream will be
$10, –$10, $15, which is less risky compared to the initial stream $15, –$15, $15.
14. Technically, the total risk of asset , can be decomposed into the systematic risk component
and the specific risk .

Page 43
Observe that as ρi,M approaches 1, total risk becomes composed of pure systemic risk.
15. r denotes the continuously compounded rate of interest. It can be derived from the annualized
discrete interest rate R by the relation r = ln (l + R).
16. See Stoll (1969). See also Galai (1977) for a characterization of options.
17. Their major paper was published in 1958 and an important correction appeared in 1963. The best
presentation and explanation of their model is found in Fama and Miller (1974). See also Miller
(1977).
18. See, e.g., Brealey and Myers (2000).
19. ARCH stands for Auto Regressive Conditional Heteroskedasticity. The G in GARCH stands for
General. See a summary of these procedures in Engle (1982) and Bollerslev (1986).
20. From 1998, the SEC required listed companies to report their exposures to market risk factors
related to their derivative positions, and to positions in other financial instruments. (See Chapter 16
for a brief description of the SEC requirements.)
21. In Chapter 15 we discuss the issue of liquidity risk and how it interplays with market and credit
risk.
22. See Chapter 2. The G-12 recommendations are intended to reduce the likelihood of another crisis
similar to that of LTCM and, perhaps more important, to reduce the impact of such an event on
market stability.
23. See, e.g., Procter & Gamble example (footnote 6).

Page 45
Chapter 2—
The New Regulatory and Corporate Environment
1—
Introduction
In Chapter 1 we discussed the importance of the regulatory environment to the development of risk
management in financial institutions. In this chapter, we take the story one step further by explaining
how sophisticated methodologies in risk management are starting to become part of the new
regulatory and corporate risk environment.
First, though, we need to ask a fundamental question. Regulators impose a unique set of minimum
required regulatory capital rules on commercial banks. Why do they do so?
Banks collect deposits and play a key role in the payment system. While the deposits are often insured
by specialized institutions (such as the Federal Deposit Insurance Corporation or FDIC 1 in the United
States, the Canadian Deposit Insurance Corporation or CDIC in Canada, etc.), in effect national
governments act as a guarantor for commercial banks; some also act as a lender of last resort.
National governments therefore have a very direct interest in ensuring that banks remain capable of
meeting their obligations: they wish to limit the cost of the ''safety net" in the case of a bank failure.2
This is one reason why the amount of capital retained by a bank is regulated. By acting as a buffer
against unanticipated losses, regulatory capital helps to privatize a burden that would otherwise be
borne by national governments.

Page 46
Moreover, in banking it seems that capital structure matters more than in other industries because of
the importance of confidence to banks, and to the financial services industry in general. Regulators try
to make sure that banks are well enough capitalized to avoid any "systemic effect," whereby an
individual bank failure would propagate to the rest of the financial system. Such a "domino effect"
would disrupt world economies and incur heavy social costs. The problem here is that banks often act
as the transmission belt on which setbacks in the financial sector are transmitted to the wider economy.
However, fixed-rate deposit insurance itself creates the need for capital regulation because of the
moral hazard and adverse selection problems that it generates. Under current regulations, insured
banks have an incentive to assume relatively more risk than if they were uninsured. This is because
fixed-rate (non-risk-based) deposit insurance is akin to a put option sold by the government to banks
at a fixed premium, independent of the riskiness of their assets. As the rate is fixed, this option
increases in value as the bank's assets become riskier. 3 Moreover, as deposits are insured, there is no
incentive for depositors to select their bank cautiously. Instead, depositors may be tempted to look for
the highest deposit rates, without paying enough attention to a bank's creditworthiness.
Prior to the implementation in 1992 of the 1988 Basle Accord, bank capital was regulated by
imposing uniform minimum capital standards. These were applied to banks regardless of their
individual risk profiles, and the off-balance-sheet positions and commitments of each bank were simply
ignored. The increased international competition among banks during the 1980s emphasized how
inconsistently banks were regulated with regard to capital. Japanese bank regulations contained no
formal capital adequacy requirements, while in the United States and the United Kingdom banks were
required to finance more than 5 percent of their risky assets by means of equity.
The major increase in off-balance-sheet activity by banks that took place in the 1980s altered the risk
profile of banks, while the regulatory requirements concerning equity ratios remained the same. The
1988 Basle Accord (known also as the 1988 BIS Accord, or the "Accord") established international
minimum capital guidelines that linked banks' capital requirements to their credit

Page 47
exposures. The Accord was intended to raise capital ratios, which were generally perceived as too
low. It was also intended to harmonize minimum capital ratios. However, the regulators focused
primarily on credit risk, and ignored market risk and other risks.
More recently, the "1996 Amendment" extended the initial Accord to include risk-based capital
requirements for the market risks that banks incur in their trading accounts. 4
Under the Accord and its Amendment, banks are currently required to satisfy three capital adequacy
standards: first, a maximum assets to capital multiple of 20; second, an 8 percent minimum ratio of
eligible capital to risk-weighted assets;5 and third, a minimum capital charge to compensate for market
risk of traded instruments on and off the balance sheet.
In addition to these capital adequacy requirements, the Bank for International Settlements (BIS) has
set limits on concentration risks. Risks that exceed 10 percent of the bank's capital must be reported,
and banks are forbidden to take positions that are greater than 25 percent of the bank's capital without
explicit approval by their local regulator.6 In addition to incorporating market risk, the 1996
Amendment officially consecrates the use of internal models based on the value-at-risk (VaR)
methodology to assess market risk exposure. (VaR modelling is discussed in detail in Chapter 5.)
The international regulators clearly intend to encourage banks to develop their own proprietary risk
measurement models to assess regulatory, as well as economic, capital. The advantage for the banks
should be a substantial reduction in regulatory capital, and a more accurate allocation of capital that
reflects the actual risk embedded in their positions, compared to the capital charge arising from the
standardized approach proposed by BIS. However, to benefit from this capital relief, the 1996
Amendment made it clear that banks must implement a risk management infrastructure that is fully
integrated with their daily risk management—in particular, with their setting of trading limits and their
risk monitoring of operations. It is not enough for banks to develop sophisticated analytical
approaches to measure and report regulatory capital. The bank's risk managers and traders should
themselves use these analytical approaches to monitor their positions and their risk limits.
This more qualitative concern with the infrastructure and application of risk measurement and
management techniques can be

Page 48
traced back to recommendations of a seminal report published by the Group of Thirty (G-30) in
1993. Section 2 of this chapter discusses these Group of Thirty recommendations, and prepares the
ground for the more detailed discussion of how to structure the price risk management functions of a
bank provided in Chapter 3.
Section 3 of this present chapter discusses the original 1988 BIS Accord. Section 4 introduces the
1996 Amendment which became mandatory in January 1998 and which is therefore now known as
"BIS 98"; again, this section prepares the reader for the more detailed comparison of the BIS 98
standardized approach versus the internal models approach provided in Chapter 4. As that chapter
demonstrates, the difference in capital charges between the two approaches is so considerable that
banks subject to the standardized approach may face a severe competitive disadvantage.
Finally, in Section 5 we discuss a consultative paper, released in June 1999 by the Basle Committee
on Banking Supervision. This paper proposes a New Capital Adequacy Framework to replace the
1988 Accord. This consultative paper will probably go through many amendments before it becomes
the new BIS 2000+ Accord. We also review the Group of 12 recommendations for the improvement
of counterparty risk management practices in the light of the severe market disruptions of August 1998
—and the near-collapse of the hedge fund Long-Term Capital Management (LTCM).
2—
Group of Thirty (G-30) Policy Recommendations
In 1993 the Group of Thirty (G-30) published a report that described 20 best-practice price risk
management recommendations for dealers and end-users of derivatives, and four recommendations for
legislators, regulators, and supervisors. The report was put together by a G-30 working group
composed of a diverse cross-section of end-users, dealers, academics, accountants, and lawyers
involved in derivatives. Their work was based in part on a detailed survey of industry practice among
80 dealers and 72 end-users worldwide, involving both questionnaires and in-depth interviews.
The policy recommendations in the G-30 report were the first comprehensive industry-led effort to
take stock of what the industry had learned, and to broaden awareness of the more suc-

Page 49
cessful approaches to price risk management. The G-30 focussed on providing practical guidance in
terms of managing derivatives business. The recommendations also offered a benchmark against which
participants could measure their own price risk management practices.
2.1—
Recommendations
The G-30 recommendations for dealers and end-users can be categorized into general policies, market
risk policies, credit risk policies, enforceability policies, infrastructure policies, and accounting and
disclosure policies (Table 2.1). Note that the terms "dealer" and "end-user" in the report do not refer
to particular types of institutions, but rather to the nature of their derivatives activity. A bank, for
instance, may participate both as a dealer and as an end-user. Likewise, some corporate end-users of
derivatives may also be involved as dealers.
2.2—
General Policies
The first G-30 recommendation relates to the role of senior management. Senior management plays a
key role in ensuring that risk is controlled in a manner consistent with the overall risk management and
capital policies approved by their Board of Directors. Clearly, these policies should be reviewed as
business and market circumstances change.
Specifically, the G-30 recommended that "policies governing derivatives use should be clearly defined,
including the purposes for which these transactions are to be undertaken. Senior management should
approve procedures and controls to implement these policies, and management at all levels should
enforce them."
2.3—
Market Risk Policies
The G-30 felt strongly that entities should have an independent market risk management function
(Recommendation 8). Specifically, the G-30 stated, that "dealers should have a market risk
management function with clear independence from the position management function." Further, they
stated that "dealers should have

Page 50
TABLE 2.1
Taxonomy of G-30 Recommendations
General policies 1. The role of senior management
Market risk (valuation, measurement, and 2. Marking-to-market
management) 3. Market valuation methods
4. Identifying revenue sources
5. Measuring market risk
6. Stress simulations
7. Investing and funding forecasts
8. Independent market risk management
9. Practices by end-users
10. Measuring credit exposure
Credit risk (measurement and management) 11. Aggregating credit exposures
12. Independent credit risk management
13. Master agreements
14. Credit enhancement
Enforceability 15. Promoting enforceability
Infrastructure (systems, operations, and controls) 16. Professional expertise
17. Systems
18. Authority
Accounting and disclosure 19. Accounting practices
20. Disclosures
Recommendations for legislators, regulators, and 21. Recognizing netting
supervisors 22. Legal and regulatory uncertainties
23. Tax treatment
24. Accounting standards
a market risk management function with clear independence and authority."
The G-30 also stressed the importance of measuring market risk in terms of a VaR measure
(Recommendation 5), as well as the importance of stress testing (Recommendation 6). Specifically, the G-
30 pointed out that "dealers should use a consistent measure to calculate daily the market risk." The G-30
also stressed that the VaR should be compared to market risk limits. The G-30 encouraged

Page 51
stress testing by pointing out that "dealers should regularly perform simulations to determine how their
portfolios would perform under stress conditions."
The G-30 further recommended that institutions should ensure that the mark-to-market process
(Recommendation 2), is rigorously conducted. Specifically, the G-30 pointed out that dealers "should
mark their derivatives positions to market at least on a daily basis for risk management purposes." The
G-30 did not provide specific guidance on how to mark a portfolio to market, but they did provide
broad market valuation guidelines (Recommendation 3). For example, they pointed out that
"derivatives portfolios should be valued at mid-market levels less specific adjustment. Mid-market
valuation adjustment should allow for expected future costs such as unearned credit spread, close-out
costs, investing and funding costs, and administrative costs."
The G-30 stressed the importance of identifying revenue sources (Recommendation 4) in terms of
managing market risk. For example, the G-30 stated that "dealers should measure the components of
revenue regularly and in sufficient detail to understand the sources of risk."
The G-30 also emphasized that "dealers should periodically forecast the cash investing and funding
requirements arising from their derivatives portfolios" (Recommendation 7).
2.4—
Credit Risk Policies
The G-30 stated that dealers and end-users "should have a credit risk management function with clear
independence and authority, and with analytical capabilities in derivatives" (Recommendation 12).
The G-30 also stated credit exposure should be measured for each derivative transaction, based on
both current and potential credit exposure (Recommendation 10). The G-30 did not provide any
specific guidance about how this calculation should be performed. Nevertheless, the G-30 pointed out
the importance of aggregating credit exposures (Recommendation 11). For example, the G-30 pointed
out that "credit exposures on derivatives, and all other credit exposures to a counterparty, should be
aggregated, taking into consideration enforceable netting arrangements. Credit

Page 52
exposures should be calculated regularly and compared to credit limits."
The G-30 also provided recommendations on credit enhancement (Recommendation 14). They
recommended that dealers and end-users "should assess both the benefits and the costs of credit
enhancement and related risk-reduction arrangements." 7 The G-30 also pointed out that if credit
downgrades trigger early termination or collateral requirements, then participants should carefully
consider their own capacities, and those of their counterparties, to meet the potentially substantial
funding needs that might result.
Trigger provisions based on downgrade or other adverse changes have the potential to create sudden
and sizeable liquidity requirements. An alternative procedure that limits this risk of unexpected
liquidity crises is the periodic cash settlement of the underlying exposure (see Chapter 12).
2.5—
Operational Risk Policies
The G-30 emphasized the control of operational risk. For example, the G-30 emphasized the
importance of hiring skilled professionals. Specifically, the G-30 pointed out (Recommendation 16)
that one should "ensure that derivatives activities are undertaken by professionals in sufficient
number and with the appropriate experience, skill levels, and degrees of specialization."
The G-30 stressed the importance of building best-practice systems (Recommendation 17). They
pointed out that one should "ensure that adequate systems for data capture, processing, settlement,
and management reporting are in place so that derivatives transactions are conducted in an orderly
and efficient manner in compliance with management policies." For example, the G-30 pointed out
that dealers and end-users "should have risk management systems that measure the risks incurred in
their derivatives activities based upon their nature, size, and complexity."
The G-30 (Recommendation 19) emphasized that accounting practices should highlight the risks
being taken. For example, the G-30 pointed out that dealers and end-users "should account for
derivatives transactions used to manage risks so as to achieve a consistency of income recognition
treatment between those instruments and the risks being managed."

Page 53
These 20 recommendations constitute the backbone of the qualitative requirements of the 1996 BIS
Amendment, as we discuss in Chapter 4.
3—
The 1988 BIS Accord:
The "Accord"
International risk-based capital adequacy standards rely on principles that are laid out in the
"International Convergence of Capital Measurement and Capital Standards" document, published in
July 1988 (cf. Basle 1988), or the "Accord." This Accord was initially developed by the Basle
Committee on Banking Supervision, and later endorsed by the central bank governors of the Group of
Ten (G-10) countries. 8 The approach is quite simple and somewhat arbitrary, and it has been the
subject of much criticism. In fact, it is really only a first step in establishing a level playing field across
member countries for internationally active banks.
It defined two minimum standards for meeting acceptable capital adequacy requirements: an assets-to-
capital multiple and a risk-based capital ratio. The first standard is an overall measure of the bank's
capital adequacy. The second measure focuses on the credit risk associated with specific on- and off-
balance-sheet asset categories. It takes the form of a solvency ratio, known as the Cooke ratio, and is
defined as the ratio of capital to risk-weighted on-balance-sheet assets plus off-balance-sheet
exposures, where the weights are assigned on the basis of counterparty credit risk.
The scope of the Accord is limited since it does not address various complex issues related to capital
adequacy, such as portfolio effects and netting. "Portfolio effects" is the term used to describe various
benefits that arise when a portfolio is well diversified across issuers, industries, and geographical
locations; naturally, a well-diversified portfolio is much less likely to suffer from massive credit losses
than is a portfolio of deals concentrated with one party, one industry, and/or one geographical area.9
Netting is a legally enforceable agreement by means of which counterparties can offset their claims
against each other on a replacement cost basis, recognizing only the net amount.10 When there are
netting agreements in place, the net exposure of the portfolio to a particular counterparty may be quite
small.

Page 54
The Accord also completely ignored the problem of setting aside capital adequacy for the tradable
securities in the trading book. For example, government holdings were excluded from the capital
calculations. In recognition of these drawbacks, the Basle Committee amended the Accord in 1996,
as we discuss in Section 4. Interest risk in the banking book and other risks, such as liquidity and
operational risks, were also disregarded. 11
Below, we review the main features of the Accord on credit risk, as it stands today after several
modifications.
3.1—
The Assets-to-Capital Multiple
A simple test for determining the overall adequacy of a financial institution's capital is the assets-to-
capital multiple. This is calculated by dividing the bank's total assets, including specified off-balance-
sheet items, by its total capital. The off-balance-sheet items included in this test are direct credit
substitutes (including letters of credit and guarantees), transaction-related contingencies, trade-related
contingencies, and sale and repurchase agreements. All of these items are included at their notional
principal amount.
At present, the maximum multiple allowed is 20. It is conceivable that a bank with large off-balance-
sheet activities might trigger this multiple as the minimum capital requirement, but in general the
assets-to-capital multiple is not the binding constraint on a bank's activities.
3.2—
The Risk-Weighted Amount Used to Compute the Cooke Ratio
In determining the Cooke ratio, it is necessary to consider both the on-balance-sheet as well as
specific off-balance-sheet items. On-balance-sheet items have risk weightings from zero percent for
cash and OECD government securities to 100 percent for corporate bonds and others. Off-balance-
sheet items are first expressed as a credit equivalent (see Section 3.3), and then are appropriately risk-
weighted by counterparty. The risk-weighted amount is then the sum of the two components: the
risk-weighted assets for on-balance-sheet instruments and the risk-weighted credit equivalent for off-
balance-sheet items. Table 2.2 gives the risk capital weights

Page 55
TABLE 2.2
Risk Capital Weights by Broad On-Balance-Sheet Asset Category (WA)
Risk Weights (%) Asset Category
0 Cash and gold bullion, claims on OECD governments such as Treasury bonds or insured
residential mortgages.
20 Claims on OECD banks and OECD public sector entities such as securities issued by U.S.
government agencies or claims on municipalities.
50 Uninsured residential mortgages.
100 All other claims such as corporate bonds and less-developed country debt, claims on non-OECD
banks, equity, real estate, premises, plant and equipment.
(WA) by asset categories, and Table 2.3 shows the weights that apply to credit equivalents by type of
counterparty (WCE).
There is an apparent inconsistency between Table 2.2 and Table 2.3, since the risk weight for corporate assets
as they relate to off-balance instruments is half that required for on-balance-sheet assets. BIS's rationale for
this asymmetry is the better quality of the corporations that participate in the market for off-balance-sheet
products. It is true that there was a time when only the most
TABLE 2.3
Risk Capital Weights for Off-Balance-Sheet Credit Equivalents by Type of Counterparty (WCE)
Risk Weights (%) Type of Counterparty
0 OECD governments
20 OECD banks and public sector entities
50 Corporations and other counterparties

Page 56
financially sophisticated corporations entered the world of derivatives, but this is no longer the case.
3.3—
Calculation of the Credit Equivalent for Off-Balance-Sheet Exposures
3.3.1—
The Case of Nonderivative Exposures
A conversion factor applies, as the notional amount of these instruments is not always representative
of the true credit risk that is being assumed; the value of the conversion factor is set by the regulators
at somewhere between zero and 1, depending on the nature of the instrument (Table 2.4). The
resulting credit equivalents are then treated exactly as if they were on-balance-sheet instruments.
3.3.2—
The Case of Derivative Positions Such as Forwards, Swaps, and Options
The Accord recognizes that the credit risk exposure of long-dated financial derivatives fluctuates in
value. The Accord methodology estimates this exposure by supplementing the current marked-to-
market value with a simple measure of the projected future risk exposure.
TABLE 2.4
Credit Conversion Factors for Nonderivative Off-Balance-Sheet Exposures
Conversion Factor (%) Off-Balance-Sheet Exposure Factor
100 Direct credit substitutes, bankers' acceptances, standby letters of credit, sale and
repurchase agreements, forward purchase of assets.
50 Transaction-related contingencies such as performance bonds, revolving underwriting
facilities (RUFs), and note issuance facilities (NIFs).
20 Short-term self-liquidating trade-related contingencies such as letters of credit.
0 Commitments with an original maturity of one year or less.

Page 57
Figure 2.1
Calculation of the BIS Risk-Weighted Amount for Derivatives
Calculation of the BIS risk-weighted amount for derivatives proceeds in two steps, as shown in
Figure 2.1. The first step involves computing a credit equivalent amount, which is the sum of the
current replacement cost when it is positive (and zero otherwise), and an add-on amount that
approximates future replacement costs.
The current replacement value of a derivative is its marked-to-market or liquidation value, when that
value is positive. (When the value is negative, the institution is not exposed to default risk as the
replacement cost of the contract is zero.)
The add-on amount is computed by multiplying the notional amount of the transaction by the BIS
required add-on factor, as shown in Figure 2.1. In Table 2.5, five categories of underlying are
considered, i.e., interest rate, exchange rate and gold, equity, precious metals except gold, and other
commodities. The add-on factor differs quite substantially from one category to another, although the
rationale for such differences is not always clear.
Interest rate contracts include single-currency interest rate swaps, basis swaps, forward rate
agreements and products with similar characteristics, interest rate futures, and purchased interest rate
options. Exchange rate contracts include gold contracts (which

Page 58
TABLE 2.5
Add-on Factors by Type of Underlying and Maturity
Exchange Rate Precious Metals
Interest Rate and Gold Equity Except Gold Other Commodities
Residual Maturity (%) (%) (%) (%) (%)
One year or less 0.0 1.0 6.0 7.0 10.0
Over one year to five years 0.5 5.0 8.0 7.0 12.0
Over five years 1.5 7.5 10.0 8.0 15.0

Page 59
are treated in the same way as exchange rate contracts), cross-currency swaps, cross-currency
interest rate swaps, outright forward foreign exchange contracts, and purchased currency
options.
Equity contracts include those based on individual stocks as well as those based on equity
indices. Table 2.5 also lists the add-on factors for precious metals contracts (except for gold),
and contracts on other commodities, such as energy products, agricultural commodities, and
base metals (aluminum, copper, and zinc). For equities and commodities the add-ons apply to
forwards, swaps, and purchased options.
For example, a $100 million five-year interest rate swap would have an add-on amount of $0.5
million, i.e., 0.5 percent × $100 million, where 0.5 percent is the add-on factor given in Table
2.5 for this instrument.
The credit equivalent amount can be interpreted as an on-balance-sheet amount for regulatory
purposes. Unfortunately, the BIS approach fails to distinguish between the credit risk of plain
vanilla swaps and that of more volatile structures, such as highly leveraged swaps. The
difficulties that can arise with respect to the latter have led to some highly public disputes, e.g.,
the $200 million five-year leveraged interest rate swap that Bankers Trust entered into with
Procter & Gamble. 12
The second step in the BIS calculation consists of calculating the amount of regulatory capital
that is related to credit risk exposure. It is derived by simply multiplying the credit equivalent
amount by the counterparty risk-weighting factor given in Table 2.3. The result of this
calculation is the final risk-weighted amount.
3.4—
Netting of Derivatives Positions
In 1995 the initial BIS agreement was modified to allow banks to reduce their ''credit
equivalent" totals provided that bilateral netting agreements are in place. According to some
surveys, netting reduces the gross replacement value of a bank's credit exposure by, on
average, half.
The BIS formula for add-on amounts became:
The add-on factors are the same as in Table 2.5. NPR denotes the net replacement ratio, which
is the net replacement cost when

Page 60
positive, or zero otherwise, divided by the gross replacement cost calculated as before, without
taking into account netting, i.e., the sum of the positive replacement cost for the transactions covered
by the netting agreement.
Note that the new BIS formula does not allow for complete off-setting even if netting agreements are
in place. It is tempting to believe that the rationale favoring a minimum add-on amount stems from
the legal risk that courts might find netting agreements unenforceable in certain jurisdictions or, if the
netting agreements are upheld, that delays in reaching a settlement might negate the benefits of
netting. However, this reasoning is not valid. Leading global financial institutions negotiated with the
BIS, arguing that mature portfolios exhibit stable ratios of net to gross mark-to-market values. It was
argued that 100 percent of this ratio should be allowed. The BIS did not agree that the ratio is stable
in the long run and therefore imposed the 40 percent minimum add-on. In effect, the formula
discounts the probable benefits of netting.
These calculations are performed by the counterparty, and then the counterparty risk weight is used to
derive the risk-weighted amount. Table 2.6 illustrates the calculations using a simple example.
3.5—
Capital and the Cooke Ratio
Banks are required to maintain a capital amount equal to at least 8 percent of their total risk-weighted
assets (as calculated in the previous section). Capital, as defined by the Cooke ratio, is broader than
equity capital. It has three components:
1. Tier 1, or core capital, which includes common stockholder's equity, noncumulative perpetual
preferred stock, and minority equity interests in consolidated subsidiaries, less goodwill and other
deductions.
2. Tier 2, or supplementary capital, which includes hybrid capital instruments, such as cumulative
perpetual preferred shares and qualifying 99-year debentures. These instruments are essentially
permanent in nature and have some of the characteristics of both equity and debt. Tier 2 capital also
includes instruments with more limited lives, such as subordinated debt with an original average
maturity of at least five years.

Page 61
TABLE 2.6
Illustration of the Calculation of the Add-on and Risk-Weighted Amounts Including Netting
Risk Capital Weight Counterparty A 20% Counterparty B 50%
Notional Add-on Notional Add-on
Add-on Factor Amount Marked-to-Market Value Amount 1988 Amount Marked-to-Market Value Amount 1988
Transaction 1 0.5% 1,000 400 5 700 –100 3.5
Transaction 2 1.5% 500 –200 7.5 1,000 200 15
Transaction 3 5% 1,000 –100 50 500 –200 25
Add-on amount 1988 (A1988) 62.5 43.5
Gross replacement cost (GR) 400 200
Net replacement cost (NR) 100 0*
NPR (=NR/GR) 0.25 0
Add-on amount 1995 (A1995) 34.375 17.4
Credit equivalent 134.375 17.4
Risk-weighted amount with netting 26.875 8.7
Risk-weighted amount without netting (400+62.5)×.2=92.5 (200+43.5)×.5=121.75
A1995 = A1988 (0.4+0.6 NPR).
Credit equivalent=NR+A1995.
* Note that "negative" replacement cost for counterparty B cannot be used to offset positive replacement costs of counterparty A. This is why it is set to zero.

Page 62
3. Following the 1996 Amendment to the original BIS Accord, banks can use a third tier of capital to
cover market risk in the trading book (but not credit risk in the banking book). Tier 3, or sub-
supplementary capital, consists of short-term subordinated debt with an original maturity of at least
two years. It must be unsecured and fully paid up. It is also subject to lock-in clauses that prevent the
issuer from repaying the debt before maturity, or even at maturity should the issuer's capital ratio
become less than 8 percent after repayment. In Chapter 4 we review in some depth how tier 3 capital
can be allocated against market risk for the trading book. 13
According to the original Accord, tier 1 and tier 2 capital should represent at least 8 percent of the
risk-weighted assets, to protect the bank against credit risk. At least 50 percent of this amount must
take the form of tier 1 capital.
In practice, capital levels of regulated banks tend to exceed these minimum requirements. In 1997 the
risk-based capital ratios for six large banks all exceeded the minimum 8 percent total requirement, as
shown in Table 2.7. In addition, at all of these banks the ratios for tier 1 capital exceeded the 4
percent minimum requirement. According to regulatory officials, the risk-based capital ratios of
almost all U.S. banks exceed the minimum required level. Interestingly, on average the top 50 insured
commercial banks in the United States already finance in excess of 2 percent their risk-weighted
assets by means of subordinated debt.14
4—
The "1996 Amendment" or "BIS 98"
In April 1995 the Basle Committee issued a consultative proposal to amend the Accord which
became known as the "1996 Amendment" or, after it was implemented, "BIS 98." This proposal was
adopted by the U.S. regulatory agencies in July 1995, and became mandatory for all U.S. financial
institutions with significant trading activities as of January 1, 1998.15 It requires financial institutions
to measure and hold capital to cover their exposure to the "market risk" associated with debt and
equity positions in their trading books, and foreign exchange and commodity positions in both the
trading and banking books.16 These positions include all financial instruments that are marked-to-
market, whether they are

Page 63
TABLE 2.7
Risk-Based Capital Ratios for Six Large Holding Companies, as of December 31, 1997
Dollars in Billions
Total Risk-Based Capital Tier 1 Risk-Based Capital
Percentage Percentage
of Total of Total
Risk-Weighted Risk-Weighted
Bank Holding Company Dollar Amount Assets Dollar Amount Assets
BankAmerica Corporation $26.6 11.6% $17.3 7.5%
Bankers Trust New York Corp. 11.0 14.1 6.4 8.3
Canadian Imperial Bank of Commerce* 14.5 9.8 10.2 7.0
The Chase Manhattan Corp. 33.3 11.6 22.6 7.9
Citicorp 31.1 12.3 21.1 8.3
First Chicago NBD Corp. 12.7 11.7 8.5 7.9
Note: All figures rounded.
* The fiscal year for the Canadian Imperial Bank of Commerce ended on October 31, 1997. The capital ratios in the table above for the Canadian Imperial
Bank of Commerce were calculated using regulatory guidelines for Canadian banks. Under U.S. rules, its ratios would have been 8.8 percent for total capital
and 6.4 percent for tier 1 capital.
Source: GAO (1998) and 1997 Annual Reports.
plain vanilla products such as bonds or stocks, or complex derivative instruments such as options, swaps, or credit derivatives. Marking
financial instruments to market must be performed for both accounting and management purposes.
The most significant risk arising from the nontrading activities of financial institutions is the credit risk associated with default. The
Accord treated all instruments equivalently, whether they reside in the trading or banking book. The 1996 Amendment introduced the
requirement of measuring market risk, in addition to credit risk, in the trading book. The initial Accord continues to apply to the
nontraded items both on-balance-sheet and off-balance-sheet, as well as to off-balance-sheet over-the-counter (OTC) derivatives. Market
risk must be measured for both on- and off-balance-sheet traded instruments. However, on-balance-sheet

Page 64
assets are subject to the market risk capital charge only, while off-balance-sheet derivatives, such as
swaps and options, are subject to both the market risk charge, and to the credit risk capital charges
stipulated in the original 1988 Accord.
To summarize, a bank's overall capital requirement is now the sum of the following:
• Credit risk capital charge, as proposed in the initial 1988 Accord, which applies to all positions in
the trading and banking books, as well as OTC derivatives and off-balance-sheet commitments, but
which excludes debt and equity traded securities in the trading book, and all positions in commodities
and foreign exchange.
• Market risk capital charge for the instruments of the trading book, on as well as off the balance
sheet. 17
In BIS 98 the authorities recognized the complexity of correctly assessing market risk exposure,
especially for derivative products. Flexibility in the modeling of the many components of market risk
is thus allowed. The most sophisticated institutions—i.e., those that already have an independent risk
management function in place, with sound risk management practices—are permitted to choose
between their own "internal VaR model," referred to as the "internal models approach," and the
"standard model" proposed by BIS, referred to as the "standardized approach," to determine the
regulatory capital that they need to set aside to cover market risk.
The new capital requirement related to market risk is largely offset by the fact that the capital charge
calculated under the 1988 Accord to cover credit risk no longer needs to be held for on-balance-sheet
securities in the trading portfolio. The capital charge for general market risk and specific risk should,
on aggregate, be much smaller than the credit risk capital charge for large trading books. Also, banks
adopting the internal models approach should realize substantial capital savings, in the order of 20 to
50 percent, depending on the size of their trading operations and the type of instruments they trade.
This is because internal models can be designed to capture diversification effects by realistically
modeling the correlations between positions. The standardized model designated in BIS 98 does not
attempt to model correlations accurately in this way.18

Page 65
The internal models approach provides for greater disclosure of trading market risks than the BIS 98
standardized model. For example, internal models make use of the fact that market risk is made up of
both "systematic risk" and "specific risk," and distinguish between these risk components. Systematic
risk, which is sometimes called "general market risk," refers to changes in market value resulting
from broad market movements. Specific risk, on the other hand, refers mainly to idiosyncratic or
credit risk. It is the risk of an adverse price movement due to idiosyncratic factors related to the
individual issuer of the security.
Highly concentrated portfolios, which have a great deal of specific risk, as shown on the left-hand
side of Figure 2.2, contain products that are highly correlated with one another. The more diversified
a portfolio, the greater the ratio of systematic to specific risk and vice versa.
The regulatory capital charge for banks using internal models for both general market risk and
specific (credit) risk is set according to the following:
Figure 2.2
Systemic Risk, Specific Risk, and the Level of Diversification

Page 66
A two-tier multiplier system applies:
• The multipliers of 3 and 4, which apply to market risk and credit risk, respectively, reward the
quality of the models. In fact these values of 3 and 4 are the minimum values that banks can currently
expect. The regulators may decide to set the multipliers anywhere between 3 and 4, and 4 and 5,
depending on how well the models capture the various aspects of market and credit risk, respectively.
• The trigger is related to the quality of the control process in the bank. This trigger is set to 8 for all
banks in North America, while it currently varies between 8 and in the neighborhood of 25 in the
United Kingdom. 19
4.1—
BIS 98 Qualitative Requirements
Before an institution can become eligible to use its own internal VaR model to assess the regulatory
capital related to market risk, it must put sound risk management practices in place. This "best
practice" risk management satisfies the standards set out in the G-30 recommendations discussed in
Section 2. The institution should have a strong risk management group which is independent from the
business units that it monitors, and which reports directly to the senior executive management of the
institution. The main features of a prototype risk management organization are discussed in Section
4.2.
The internal model should not be used only for calculating regulatory capital, but should be fully
integrated into the daily risk management of the institution. Models should also be used to set limits,
allocate economic capital to business units, and measure performance via risk-adjusted return on
capital (RAROC) calculations (as explained in Chapter 14). In addition the regulators require that
systematic backtesting and stress testing be conducted on a regular basis, in order to test the
robustness of the internal model to various extreme market conditions and crises. Improvements
should be implemented if the model fails to pass the tests, e.g., when backtesting reveals that trading
losses are happening more frequently than the VaR calculation would suggest.
Implementing a VaR model is a significant endeavor. The aim, ultimately, is to build a truly
integrated, global, real-time system

Page 67
that records all positions centrally in a data warehouse, and which maps these positions in terms of
their "risk factors;" as we explain in more detail in Chapter 5, risk factors are a vital component of the
VaR calculation. Part of the challenge of implementing such a system is ensuring that the model
inputs, and therefore the risk measures, are reliable and accurate:
• A formal vetting system is needed to approve the models and their modifications, assumptions, and
calibration.
• Model parameters should be estimated independently of the trading desks to avoid the temptation
by the traders to "fudge" volatility numbers and other key parameters to make their positions smaller.
• The financial rates and prices which feed the risk management system should come from sources
independent of the front office, and be located in a financial database independently controlled by
risk management.
4.2—
Best-Practice Risk Management
The Board and the bank's senior management have the primary responsibility to ensure that the bank
implements a best-practice risk management system. "Best practice" can be usefully discussed in
relation to the G-30 recommendations listed earlier in this chapter.
Senior managers play a critical role in establishing a corporate culture in which best-practice risk
management can flourish. They need to encourage the implementation of best-practice risk
management in order to control risk and provide the appropriate risk oversight for their dealing
rooms. Dealers and risk management personnel will ultimately behave in a way that is related to the
rewards offered to them by senior management. A challenge for senior management is to harmonize
the behavior patterns of dealers and risk managers, and to create an environment in which both sides
cooperate.
The trade-off between maximizing short-term revenue and the incremental expense required to
control risk requires delicate balancing. To achieve best-practice risk management banks will often
have to invest in longer-term risk management projects whose

Page 68
benefits will not accrue for several years. Significant pressure to build revenue in lean years often
serves to discourage this kind of long-term investment. Instead, the risk manager in low-corporate
governance banks is typically asked to install necessary risk controls for the "least possible" cost.
Unfortunately, short-term revenue maximization is often diametrically opposite to the behavior
required to encourage first-class risk management.
Senior management in banks must make sure that risk managers are skilled so that compensation
systems between dealers and risk managers can be harmonized. Risk managers themselves need to be
adequately rewarded if the bank is to attract the best talents to its risk management function.
Otherwise, talent will simply flow from the risk management function to the business functions.
Many organizations dealing in financial instruments have not invested in establishing appropriate
policies or in developing appropriate risk methodologies. Chapter 3 offers an overview of the kind of
organizational environment that facilitates best-practice risk management. Specifically, Chapter 3
presents the framework for risk management in terms of "three pillars": best-practice policies, best-
practice methodologies, and best-practice infrastructure.
Senior managers need to encourage the development of integrated systems that aggregate the various
risks (market risk, credit risk, liquidity risk, operational risk, etc.) generated by their businesses in a
consistent framework across the institution. This may be a necessary condition to obtain regulatory
approval of internal models. An environment where each business unit calculates their risk separately
with different rules will not provide a meaningful oversight of firm-wide risk. The increasing
complexity of products, the linkages between markets, and the potential benefits offered by portfolio
effects are pushing risk-literate organizations toward standardizing and integrating their risk
management. Dealers and risk managers need an integrated price risk management capability to
ensure that their returns (net profits) outweigh the risks that they take.
5—
The BIS 2000+ Accord
The BIS 1988 rules are generally acknowledged to be flawed. First, as we noted earlier, the Accord
does not address complex issues

Page 69
such as portfolio effects, even though credit risk in any large portfolio is bound to be partially offset
by diversification across issuers, industries, and geographical locations. For example, a bank is
required to set aside the same amount of regulatory capital for a single $100 million corporate loan as
for a portfolio of 100 different and unrelated $1 million corporate loans.
Second, the current rules assume that a loan to a corporate counterparty generates five times the
amount of risk as does a loan to an OECD bank, regardless of their respective creditworthiness. For
example, a loan to General Electric Corporation, an AAA-rated entity, has to be supported by five
times as much regulatory capital as a similar loan to a Mexican (BB) or Turkish bank (B). General
Electric is also considered to be infinitely more risky than the sovereign debt of Turkey or Mexico.
Clearly, this is the opposite of what one might think appropriate.
Third, regulatory rules assume that all corporate borrowers pose an equal credit risk. For example, a
loan to an AA-rated corporation requires the same amount of capital as a loan to a B-rated credit. This
is also clearly inappropriate.
Fourth, revolving credit agreements 20 with a term of less than one year do not require any regulatory
capital, while a short-term facility with 366 days to maturity bears the same capital charge as any
long-term facility. The bank is clearly at risk from offering short-term facilities, yet so long as the
term is less than one year no regulatory capital is required. This has led to the creation of the ''364-day
facility," by means of which some banks commit to lend for 364 days only, although the facility is
then continuously rolled over. Such a facility attracts no capital charge, even if the terms of the
facility are such that if the commitment is cancelled, the obligor has the right to pay back the drawn
amount over a number of years.
Finally, as we previously discussed, the Accord does not allow sufficiently for netting and does not
provide any incentive for credit risk mitigation techniques such as the use of credit derivatives.
These shortcomings have produced a distorted assessment of actual risks and have led to a
misallocation of capital. In some instances, they have even led financial institutions to take on too
much risk. The problem is that as the definition of regulatory capital drifts further away from the
bank's understanding of the economic capital needed to support a position, the bank faces a

Page 70
strong incentive to play the game of "regulatory arbitrage." Banks are tempted to incur lower capital
charges while still incurring the same amount of risk by using financial engineering tricks such as
securitization (through various types of collateralized debt obligations, or CDOs, and the use of credit
derivatives). In the process, banks transfer high-grade exposures from their banking book to their
trading book, or place them outside the banking system. This means that the quality of the assets
remaining on the books of a bank deteriorates, defeating the purpose of the Accord.
These problems have led the banking industry to suggest that banks should be allowed to develop
their own internal credit VaR models, in lieu of the 1988 BIS Accord. They would use these
regulator-approved models to calculate the minimum required regulatory credit risk capital associated
with traditional loan products located in the banking book. This would be the credit risk equivalent of
the BIS 98 Accord we discussed earlier, which allowed banks to use approved internal models for
determining the minimum required regulatory capital for market risk.
Over the last five years, a series of industry-sponsored credit VaR methodologies have been devised,
including CreditMetrics (developed by investment bank JP Morgan) and CreditRisk + (developed by
Credit Suisse Financial Products, now Credit Suisse First Boston or CSFB). Credit VaR models have
also been developed by various software and consultancy firms: The KMV approach to model
expected default frequencies is now in use at many U.S. financial institutions, and has added much
value in terms of advancing the practical utility of using a model-based approach to credit risk. All
these models are reviewed in much more detail in Chapters 8, 9, and 10. Here, it is worth noting that
a major challenge facing every model developer is to ensure that proprietary credit VaR formulas are
comprehensible and practical enough to be accepted by the regulatory community.
With the advent of products such as credit derivatives, the financial community is moving towards
valuing loans and loan-type products on a mark-to-model basis. Moreover, there is a trend toward
applying quantification techniques similar to those used to measure market risk to the measurement of
credit VaR—especially in the case of products whose value is mostly driven by changes in credit
quality.
A related but separate challenge is to develop an integrated approach to calculating market VaR and
credit VaR. For example,

Page 71
typically most financial institutions use one set of rules to value trading products and another set of
rules to value loan products. The integration of market VaR and credit VaR is at the leading edge of a
new wave of risk management. One model for an integrated risk measurement approach builds on the
Black–Scholes theoretical framework and related work by Robert Merton. (Merton and Scholes won
the Nobel Prize in Economics in 1997 for their work on the "valuation of contingent claims." 21)
Merton's model (1974) is becoming the industry-standard approach for the estimation of credit VaR;
in fact, the CreditMetrics and KMV models we mentioned above both use Merton's model as the
theoretical foundation for their credit VaR models.
Developing an integrated model will have important implications from both a risk transparency and a
regulatory capital perspective as the banking industry moves into the twenty-first century. This is
because simply adding market VaR to credit VaR to obtain total VaR, rather than developing an
integrated model, greatly overstates the amount of risk. Summing the values ignores the interaction
or correlation between market VaR and credit VaR. We expect that, over time, regulators will move
to allow banks to use their own internal credit VaR model, in lieu of the standardized BIS 1988 rules.
Eventually, they will also move toward an integrated risk model that encompasses both market VaR
and credit VaR. From this point, it will be possible to envisage a truly integrated price risk
framework that risk managers will be able to use to generate both regulatory capital and economic
capital (Figure 2.3).
5.1—
A New Capital Adequacy and Credit Risk Modeling Framework:
The 1999 Consultative Papers
Global competition is now affecting banks in emerging market countries. Regulators need to make
sure that the regulatory framework does not inadvertently drive a competitive wedge between G-10
and non-G-10 competing banks. Over, the last 10 years the risk profile of banks has changed
dramatically. Its composition and complexity, and the methodologies used to describe risks, now
make strong supervision and enhanced market discipline important complements to capital
regulation.22 Finally, the banks' regulators realize that there is an urgent need to revise the 1988

Page 72
Figure 2.3
Integrated Risk Models
Accord to eliminate the kind of regulatory arbitrage we mentioned earlier. This can only be achieved
by a better alignment of regulatory and economic capital.
Banks' regulators also recognize that the biggest risk facing commercial banks is the oldest risk of all,
i.e., credit risk, rather than the risk of rogue traders losing fortunes in the capital markets. Recent
high-profile trading losses, even including the significant losses to Barings Bank at the hands of Nick
Leeson, amount to a few billion dollars. The damage caused by reckless lending at Credit Lyonnais in
the 1980s amounted to more than $20 billion. The credit losses incurred by banks in Japan and East
Asia will reach hundreds of billions of dollars.
In June 1999 the Basle Committee on Banking Supervision (BIS) issued a proposal for a new capital
adequacy framework to replace the 1988 Accord. The consultation process with banks and various
industry groups will continue until March 2000.
The objectives of the New Accord are to:
• Promote safety and soundness in the financial system by maintaining at least the same level of
capital as banks maintain in today's system. 23
• Enhance competitive equality. The new rules should not offer incentives for regulators in some
countries to make

Page 73
their rules more attractive to banks to attract investment in the industry in their country. Two banks
with the same portfolios should hold the same capital wherever they are located.
• Constitute a more comprehensive approach to risks, to eliminate the criticisms of the 1988 Accord,
and to cover more risk types such as interest rate risk in the banking book and operational risk.
• Focus on internationally active banks. However, the principles governing the approach should be
suitable for application to banks of varying levels of complexity and sophistication. 24
To achieve these objectives, the Basle Committee proposes a framework that rests on three pillars
(Figure 2.4):
• Minimum capital requirements. The objective is to propose a new standardized approach: the
default approach basing risk weights on available external credit ratings. The most sophisticated
banks will be allowed to use alternative
Figure 2.4
The Three Pillars of the New Approach

Page 74
models based on the use of their own internal credit ratings. Critical issues, however, include how to
validate a bank's internal risk ratings and how to link risk weights to these internal ratings so as to
ensure economically meaningful and reasonably consistent capital treatment of similar risks across
banks. The most sophisticated banks may also be allowed to use portfolio credit models when data
limitation and validation issues have been satisfactorily addressed.
• Supervisory review process to ensure that banks follow rigorous processes, measure their risk
exposures correctly, and have enough capital to cover their risks. Regulatory arbitrage will be
scrutinized.
• Market discipline as a lever to strengthen the safety and soundness of the banking system through
better disclosure of capital levels and risk exposures, to help market participants to better assess the
bank's ability to remain solvent.
5.1.1—
The First Pillar:
Minimum Capital Requirements
The new approach to minimum capital requirements can be thought of as a ladder with three rungs
(Figure 2.5):
• An improved standardized approach.
• A kind of simplified modeling approach, based on the bank's internal ratings.
• A more sophisticated full modeling approach. In effect, this will extend to the banking book the
more sophisticated approaches that banks are already allowed to use for their trading accounts. 25
A—
Standardized (or Default) Approach
The Basle Committee proposes to improve the 1988 BIS standardized approach by:
• Better differentiating among various credits through the use of external credit assessments,
particularly for loans in the banking book; there will still be no provision to allow banks to capture
portfolio effects.

Page 75
Figure 2.5
Minimum Capital Requirements
• Incorporating new risk categories, such as interest risk in the banking book and operational risk.
• Adding a capital charge for other risks such as liquidity, legal, and reputational risks.
• Better recognizing and factoring in credit mitigation techniques.
For credit risk, the new weighting scheme proposed for claims on sovereigns, banks, and
corporations is summarized in Table 2.8, where the Standard & Poor's methodology has been chosen
for the sake of illustration.
Claims on Sovereigns
Claims on sovereign credits and central banks determined to be of the highest credit quality might be
eligible for a zero-risk weight (AAA to AA, according to Standard & Poor's rating system). There are,
however, some reservations about the performance of rating agencies in assessing the rating of
borrowers that are less than ultra-prime credits. Export insurance agencies in the G-10 countries may
be used as a dual source of credit assessment for sovereigns. Note that sovereigns, banks, and
corporations rated below B+ receive a risk weight of 150 percent. 26
Claims on Banks
Two options are proposed for claims on banks. The first option attributes to claims on banks a risk
weight that is based on the

Page 76
TABLE 2.8
Risk Weights for Claims on Sovereigns, Banks, and Corporations, Based on Standard & Poor's Rating Methodology
Assessment
Claim AAA to AA– A+ to A– BBB+ to BBB– BB+ to B– Below B– Unrated
Sovereigns 0% 20% 50% 100% 150% 100%
Banks Option 11 20% 50% 100% 100% 150% 100%
Option 22 20% 50%3 50%3 100%3 150% 50%3
Corporations 20% 100% 100% 100% 150% 100%
1 Risk weighting based on risk weighting of sovereign in which the bank is incorporated.
2 Risk weighting based on the assessment of the individual bank.
3 Claims on banks of a short original maturity, for example less than six months, would receive a weighting that is one category more favorable than the usual risk weight on the bank's claims.

Page 77
weighting of the sovereign country in which the bank is incorporated. The weight is one notch less
favorable than that applied to the sovereign, with a cap at 100 percent, except for claims on the
lowest-rated banks (below B– in Standard & Poor's methodology), where the risk weight is set at 150
percent. For example, a claim on an AA bank would receive a risk weight of 20 percent, which
corresponds to the risk weight of a sovereign of the credit category just below (i.e., A+ to A–).
The second option would be to use a rating assigned directly to the bank by an external rating agency.
In this case, a maturity element is added to the framework. Claims on banks of a short original
maturity, e.g., less than six months, would receive a risk weight that is one category more favorable
than the usual risk weight on the bank's claim. For example, if a claim on a bank is normally
weighted at 50 percent, a short-term claim on that bank would receive a risk weight of 20 percent.
The floor on all banks' claims is 20 percent, and no claim on a bank could receive a risk weight less
than that applied to its sovereign.
Claims on non-central-government public sector entities and securities firms would be weighted in
the same way as claims on banks.
Claims on Corporations
For claims on corporations, the new Accord proposes to retain a risk weight of 100 percent except for
highly rated companies, i.e., those rated AAA to AA–. Highly rated companies would benefit from a
lower risk weight of 20 percent. Short-term revolvers with a term of less than a year would be subject
to a capital charge of 20 percent, instead of zero percent under the 1988 Accord. The new proposal
would put highly rated corporate claims on the same footing as the obligations of bank- and
government-sponsored enterprises.
What is not clear at this stage is whether the risk weights apply to the issuer rating or the facility
rating. Naturally, the banking industry was hoping that there would be more granularity in the
differentiation between corporate credits. In the proposed framework, an investment-grade firm rated
A+ and a speculative firm rated BB+ would receive the same risk weight of 100 percent.
Unfortunately, this proposal will not eliminate the current incentives for regulatory arbitrage. Figure
2.6 compares capital weights

Page 78
Figure 2.6
Capital Weights According to the New Proposed Capital Accord Versus CIBC's
Internal CreditVaR Model
according to the new proposal to those generated by CIBC's internal credit value-at-risk model, 27 for
a well-diversified portfolio of corporate loans. There is a huge discrepancy between the figures for
economic capital produced by CIBC's internal model and the capital charges arising from the new
BIS proposal.
Companies rated below B– would receive a risk weight of 150 percent, according to the proposals,
while unrated companies would receive a 100 percent risk weight. This does not make much sense
since there is no incentive for companies rated B– and below to obtain a rating. Clearly, the highest
risk weight should apply to any firms that elect to remain unrated.
Loans Secured by Property
For loans secured by property the new Accord proposes a different treatment for residential
mortgages, which would continue to be weighted at 50 percent, while mortgages on commercial real
estate would, in principle, be attributed a 100 percent weighting of the loans secured.

Page 79
Asset Securitization
The new Accord addresses the issue of the credit quality of obligations secured on a pool of assets,
and issued through the medium of special purpose vehicles (SPVs), provided these obligations have a
credit rating. The Basle Committee proposes to use an external ratings-based approach to measure the
relative exposure to credit risk and determine the associated risk weights. Those rated B+ or below,
and the first loss positions, would be deducted from capital, or equivalently would be applied a risk
weight of 1250 percent so that the capital charge is 100 percent, i.e., 12.5 *8 percent (Figure 2.7).
The tranches of the obligations that are rated below investment grade (BB+ and BB–) would receive a
higher risk weight (i.e., 150 percent) than regular bond holdings with the same rating. This does not
address the issue of regulatory arbitrage. The elimination of regulatory arbitrage will follow naturally
from the convergence of economic and regulatory capital. Taxing the CLO tranches below investment
grade may eliminate the use of securitization for regulatory arbitrage purposes, but will also
discourage banks from using asset securitization to manage and mitigate credit risk.
Off-Balance-Sheet Items
No changes are contemplated to the current treatment of off-balance-sheet items, except in the case of
the credit conversion factors that apply to loan commitments (Table 2.9). Under the current
Figure 2.7
Asset Securitization

Page 80
Table 2.9
Credit Conversion Factors for Loan Commitments
Current Treatment Proposal
0% for original maturity of up to one year 20% for business commitments
0% for commitments that are unconditionally cancellable 0% for unconditionally cancellable commitments
50% for original maturity one year and over
Accord banks can avoid any capital charge on loan commitments by structuring these commitments so that
they run for a term of less than 365 days. The new proposals remove this loophole.
The Basle Committee is proposing to increase the short-term commitment risk weight to 20 percent unless
the instrument is unconditionally cancellable or can be cancelled automatically by the bank without prior
notice due to deterioration in the borrower's creditworthiness.
High-Risk Categories and Other Claims
There is a 150 percent risk weight for instruments rated below B–, whether these are issued by sovereigns,
banks, or corporations, and securitization tranches that are rated BB+ and BB–.
For all other assets the 100 percent risk weighting would continue to apply.
Issues with External Credit Ratings
Moody's, Standard & Poor's, and most of the other rating agencies in the United States have a long and
good track record for accurately rating investment-grade obligors. The industry track record is much
shorter, and not as convincing, for the rating of sovereigns and corporations with sub-prime ratings. The
Basle Committee has set out a list of criteria for eligible credit assessment institutions such as: objectivity,
independence, transparency, credibility, resources, and recognition by the national supervisor.
The question also arises as to whether credit assessments might be produced using market data, such as
credit spreads. Such an ap-

Page 81
proach might rely on option pricing methodologies such as Merton (1974), Duffie and Singleton
(1994), or Jarrow and Turnbull (1995).
B—
Internal Ratings-Based Approach
As of late 1999, the proposals for an internal ratings-based approach are still very sketchy. Before the
proposals are refined, banks' internal rating systems will need to be examined more thoroughly, and
the industry will need to evaluate various methodologies for linking capital requirements to internal
ratings. For example, banks could map their internal rating categories to Moody's and Standard &
Poor's rating systems and then to the standardized risk weights given in Table 2.8. This is not
satisfactory as it would dilute all the proprietary information on individual obligors accumulated by
banks. The Basle Committee could also design a capital charge that explicitly reflects banks'
estimates of possible credit losses. A better approach would combine a bank's internal rating system
and credit portfolio models to attribute capital to each facility on the basis of its risk contribution to
the overall risk of the portfolio. The capital weights could be based on the average of the risk
contributions for several well-diversified representative portfolios and the use of various well-
established credit models. This would present the advantage of setting ''standard" capital weights that
capture some portfolio effects. 28
While it makes a lot of sense to factor in the internal information that banks have on their
counterparties, especially for small- to medium-sized companies, a way would have to be found of
ensuring consistency in internal credit rating across different banks.
For example, the following issues would have to be addressed:
• What is the meaning of placing an entity in category xyz?
• Does it mean that the obligors in this category exhibit an expected default probability (EDF) within
a prespecified range?
• Or, is the rating associated with an expected loss given default?
• What is the horizon over which these estimations are derived? For example, for the rating system to
be consistent with the credit migration approach to modeling credit risk (as described in Chapter 8),
each rating class

Page 82
should correspond to a range of default probabilities over a one-year period.
The internal risk ratings-based approach has many practical implications for supervisors. Some key
considerations will have to be addressed when assessing a bank's rating system:
• Are the number of gradations appropriate to the range of risks incurred by the bank?
• What is the role of the internal rating system in the management process? Credit ratings are a basis
for regular risk reports to senior management and boards of directors. They are also the basis for
continuous loan review processes, under which large credits are reviewed and regraded at least
annually in order to focus attention on deteriorating credits well before they become problems.
• Is the rating process independent of credit approval and pricing functions? How often should the
ratings be updated?
• How can regulators provide a linkage to the concept of "measurable loss," and how can they
translate a rating into a capital charge? Should internal ratings be mapped into the regulatory
bucketing scale (0 percent, 20 percent, 50 percent, 100 percent, 150 percent) or into an expanded
version of it?
• Are all appropriate risk factors incorporated?
• How can regulators compare different internal rating systems? For the new proposal to be
applicable, and to maintain a level playing field, it will be necessary to ensure that internal rating
systems across banks and countries are consistent with one another.
• How can regulators backtest an internal rating system? Do the losses behave as expected?
Notwithstanding these issues, the use of the internal ratings-based approach would pave the way to
the adoption of full credit risk modeling for the banking book. It is a promising signal of the
regulators' willingness to bring regulatory capital closer to economic capital.
C—
Credit Risk Modeling
The Basle Committee issued a companion paper on April 21, 1999, analyzing current practices in
credit risk modeling. This report as-

Page 83
sesses the potential uses of credit risk models for supervisory and regulatory capital purposes.
Before any model can be approved to report regulatory capital for any asset class, the Committee
would have to be confident that the model is being used to actively manage the risks, set limits, and
allocate economic capital to the various business units. Unlike market risk, for which the
measurement models are all essentially very similar, the underlying conceptual frameworks for
models that measure credit risk are quite different. This raises some challenging issues:
• Are these models conceptually sound and do they capture accurately all the dimensions of credit
risk?
• Do these models produce similar results for the same portfolios? 29
• Are the data available to run these models, e.g., spread curves for different rating categories,
recovery rates, usage given default, default probabilities and migration frequencies, and asset return
correlations? In addition, credit data such as default probabilities are not stationary and vary with the
credit cycle. The scarcity of data and their lack of accuracy in some instances underscores the need to
better understand the models' sensitivity to structural assumptions and key parameters.
• How can credit VaR models be validated when the horizon is one year, and default data are so
relatively scarce?30 As a practical matter, empirically validating models might not be feasible.
Instead, it might be more realistic and meaningful to validate input parameters and assumptions such
as loss given default and default rates.31
• Can we feel comfortable with capital charges calculated by a model even when they differ
substantially from those generated by the standardized approach?
While these issues constitute significant hurdles, regulators are strongly encouraging banks to start
working on credit risk modeling for the banking book. Regulators recognize that only the credit risk
modeling approach will allow banks to manage concentration risk in a portfolio context. Models offer
the natural

Page 84
framework to assess the hedging efficiency of various credit risk mitigation techniques, such as the
use of credit risk derivatives, in a portfolio context. 32
Furthermore, only credit risk modeling can bring regulatory capital into closer alignment with the true
riskiness of the underlying portfolio, and therefore with economic capital. Some regulators, such as
the FSA (Financial Services Authority) in the United Kingdom, are committed to rewarding banks
that use credit risk models for allocating economic capital to their loan book by reducing the trigger
ratio which currently applies to the banking as well as the trading books.
D—
Credit Risk Mitigation Techniques
State-of-the-art credit risk management relies on credit mitigation techniques such as the use of
collateral, guarantees, credit derivatives, and on-balance-sheet netting (Figure 2.8). The current
Accord only partially recognizes collateral, guarantees, credit derivatives, and on-balance-sheet
netting agreements (when they are legally enforceable).
The new proposal acknowledges the benefits that can be derived from the use of credit mitigation
techniques and the key role they can play in active credit risk management. Just as foreign exchange
derivatives allow corporations to transfer part of their foreign exchange risk exposure to third parties
in the global markets, credit derivatives allow banks to achieve the same objective with regard to
credit risk exposures. The end result should
Figure 2.8
Credit Mitigation Techniques

Page 85
be a reduction in the concentrations of credit risk in the banking industry.
The issue of how to treat imperfect hedges needs to be addressed. Residual risks deriving from
imperfect hedges take different forms, such as:
• Maturity mismatch when the hedging instrument expires before the underlying asset. Should
regulators allow for recognition if there is a mismatch in maturities? In the case of credit derivatives,
how should regulators account for the forward risk beyond the maturity of the derivative? Should
regulators charge capital to cover this risk, or ignore it?
• Basis risk, e.g., when the exposure and the hedging instrument are subject to market risks that have
different sensitivities, which could create a shortfall in the value of the hedge. For example, if the
bank is using collateral, how should regulators account for liquidity risk? What level of "hair cut," or
adjustment, should regulators apply?
• Asset mismatches can occur when an asset is hedged by means of a credit derivative that is
referenced to an asset with different risk characteristics. How should regulators factor in correlation
risk?
E—
Treatment of Other Risks in the Banking Book:
Interest Rate Risk and Operational Risk
The current BIS 88 Accord only explicitly recognizes credit risk in the banking book. The new
Accord intends to expand risk coverage to incorporate other major sources of risks, namely interest
risk in the banking book and operational risk. Other risks may be considered such as settlement risk,
legal risk, reputational risk, and macroeconomic risks.
Simply adding together any capital charges related to these individual risks leads to an overestimation
of the capital that is needed. The key question here is how banks can validate the level and nature of
the portfolio effects that occur between risk classes.
Interest risk capital charges would only apply to banks where interest rate risks in the banking book
are significantly above average ("outliers"). This raises the question of quantifying the

Page 86
duration of core deposits. The problem of how to define what we mean by outliers also needs to be
worked out.
F—
Consistency between the Methodologies Developed for the Banking and Trading Books
The regulators will review the treatment of the trading account to ensure consistency with the
methodologies developed for the banking book (in order to reduce the incentive for regulatory
arbitrage). One interesting issue is how to incorporate liquidity risk into the risk measurement
frameworks, so as to allow for a differing treatment of the various instruments in both the trading
account and the banking book.
5.1.2—
The Second Pillar:
The Supervisory Review Process
The supervisory review process of capital adequacy should ensure that a bank's capital position and
strategy are consistent with its overall risk profile. Early supervisory intervention will be encouraged
if the capital is thought not to provide a sufficient buffer against risk. 33 The following principles are
relevant to the supervisory review of a bank's capital adequacy.
Capital above Regulatory Minimum
Supervisors should have the ability to require banks to hold capital in excess of minimum regulatory
ratios depending on a variety of factors such as the experience and quality of its management and
control process, its track record in managing risks, the nature of markets in which the bank operates,
and the volatility of its earnings. In assessing capital adequacy the regulators will have to consider the
effects of business cycles and the overall macroeconomic environment, as well as the systemic impact
on the banking system should the bank fail.34
One could envisage a system similar to that which the FSA has put in place, which makes use of an
additional multiplier, the "trigger," which applies on the top of the minimum regulatory capital.
Before such a process could be implemented, regulators need to define a sound conceptual
framework for the determination of banks' capital adequacy. The key questions here are: How can
"soundness" be defined and quantified? What is the minimum

Page 87
acceptable soundness level, and how can regulators be sure that a bank operates above this minimum
soundness level?
To be consistent with the RAROC methodology (as described in Chapter 14), soundness should be
defined as the probability of insolvency over a one-year horizon. Minimum soundness then becomes
the insolvency probability consistent with an investment-grade rating for the bank, i.e., BBB or better.
Most banks currently target an insolvency probability of four to five basis points, which is consistent
with an AA rating.
The danger of the proposed approach is that determinations of capital adequacy on a bank-by-bank
basis will prove to be arbitrary and inconsistent.
Banks' Internal Assessment of Capital Adequacy
Under the new Accord, all internationally active banks will be expected to develop internal processes
and techniques to carry out a self-assessment of their capital adequacy in relation to objective and
quantifiable measures of risks. Banks should perform comprehensive and rigorous stress tests to
identify possible events or changes in market conditions that could have an adverse effect on the
bank.
The Supervisory Process
The new Accord will impose a close partnership between banks and their supervisors. Supervisors
are expected to become familiar with the increasingly sophisticated techniques developed by the
banks to assess and control their risks. They also should be involved in the development of those
techniques.
It is clear that the position of banks' supervisor will become more challenging under the new
proposal. Regulatory agencies should therefore engage in an active program of recruiting and
educating their new generation of supervisors.
The Supervisory Intervention
The need for early intervention reflects the relatively illiquid nature of most bank assets and the
limited options that banks have when they try to raise capital quickly.
5.1.3—
The Third Pillar:
Market Discipline
The Basle Committee intends to foster market transparency so that market participants can better
assess bank capital adequacy. New

Page 88
requirements will be set regarding disclosures of capital levels, including details of capital structure
and reserves for credit and other potential losses, risk exposures, and capital adequacy (Figure 2.9).
These recommendations are likely to follow the guidelines published in September 1998 by the Basle
Committee on "Enhancing Bank Transparency." The Committee recommended that banks provide
timely information across six broad areas: financial performance; financial position (including
capital, solvency, and liquidity); risk management strategies and practices; risk exposures (including
credit risk, market risk, liquidity risk, operational risk, legal risk, and other risks); accounting
policies; and basic business, management, and corporate governance information. These disclosures
should be made at least annually, and more frequently if necessary. These recommendations have
also been adopted by the G-12.
Certain issues related to disclosure need to be addressed:
• Should the banks report risks using market-value accounting or risk-value accounting? These two
methods may produce divergent figures. For example, a written option or a swap may have a zero
marked-to-market value, while the potential future exposure of these instruments may be substantial.
• Effective disclosure cannot be achieved unless banks document internally their risk measurement
and management procedures, such as internal credit rating process, measurement of loss distributions,
and internal economic capital attribution. It is
Figure 2.9
Market Discipline

Page 89
expected that these requirements will be enforced in the new regulatory review process.
• Shareholders and debt holders have divergent objectives, the interests of the debt holders being
more aligned with the goals of the regulators. In this context, the Federal Reserve is contemplating
obliging large banks to issue subordinated debt, a form of debt that is particularly effective in
increasing market discipline. First of all, subordinated debt is the most junior of all bank liabilities.
Therefore, these bondholders are the least likely to be bailed out in the event of bank failure, and the
most likely to demand disclosures of a bank's condition. Second, subordinated debt holders do not
participate in the upside gains associated with risk taking. Hence, the primary and secondary market
spreads on subordinated debt should directly reflect the bank's expected default probability. The
issues of who will buy these subordinated bonds and whether the market for these bonds be liquid
enough for the spreads to be informative about the bank's actual probability of default still need to be
addressed.
5.2—
G-12 Recommendations for the Improvement of Counterparty Risk Management Practices
In January 1999 a group of 12 internationally active financial institutions, together with a number of
other market participants including insurance companies, hedge funds, investment management
companies, industry associations, and law firms, formed the "Counterparty Risk Management Policy
Group" or what is now known as the "G-12."
The formation of the group was inspired by the near-collapse of the hedge fund Long-Term Capital
Management (LTCM) during August 1998. In August 1998, after the Russian government had
defaulted on its debt, liquidity suddenly evaporated from many financial markets, causing asset
prices to plunge and producing large losses for many financial institutions. By September 1998
LTCM, which had built up huge market exposure by borrowing from major financial institutions, was
on the brink of collapse. It was rescued only by means of a $3.6 billion cash injection. The cash came
from 14 financial institutions coordinated by the Federal Reserve

Page 90
Bank of New York. 35 The rescue was motivated by the fear that the collapse of LTCM would not
only leave these institutions with heavy losses but would also threaten financial stability (Chapter 15
offers a more detailed discussion of the collapse of LTCM).
The objective of the G-12 was to make a comprehensive set of recommendations to reduce the
likelihood of such events in the future and, perhaps more importantly, to reduce the impact of such
events by improving the management of such failures. Some of the recommendations were intended
to make it easier to liquidate a failed institution; this sent the message to the world that no financial
institution is "too big to fail" anymore.
The recommendations published by the G-12 comprise a framework of six major building blocks:36
• Enhanced information sharing between counterparties, both prior to engaging in dealings likely to
generate significant credit exposure, and on an ongoing basis. If banks are to improve information
sharing they must address the issue of confidentiality, e.g., the net asset value of a fund, its liquidity
position, detailed portfolio composition, and collateral margin calls.37
• Integrated analytical framework for evaluating the effects of leverage on market risk, funding
arrangements and collateral requirements, asset liquidity risk, and credit risk. This framework should
consider the interplay between these factors not only under normal market conditions but also under
stressful conditions when the impact of leverage is magnified.
• Liquidation-based measures of potential counterparty credit exposures that integrate market,
liquidity, and credit risk factors. The framework for stress testing should encompass liquidity,
market, and credit risks in an integrated model. Mark-to-market replacement values should be
supplemented by different measures of liquidation-based replacement values, which incorporate the
potential for adverse price movements during the liquidation period. Limits should be set against
these various exposure measures.
Stress testing should assess concentration risk to both a single counterparty and to groups of
counterparties,

Page 91
correlation risk among both market risk factors and credit risk factors, and the risk that by liquidating
its positions the bank might move the market.
• Strengthen internal credit practices by factoring potential liquidation costs into limit-setting and
collateral standards.
• Enhancements in the quality of information provided to senior management and Board of Directors.
Senior management should convey clearly information on its overall tolerance for risks, including
loss potential in adverse markets. This information should be approved by the Board of Directors.
• Voluntary disclosure of statistical information to the regulatory authorities as well as the market
participants. 38
• Improvements to, and harmonization of, standard industry documents, as well as better internal
controls around documentation.
This report constitutes a tacit recognition that, in the past, standards have been inadequate. The
LTCM crisis would have been unlikely to have reached such extreme proportions had all these
safeguards and recommendations been in place at the time.
Notes
1. The creation of the Federal Deposit Insurance Corporation (FDIC) in 1933 provided unconditional
government guarantees for most bank creditors. The fixed-rate (non-risk-based) deposit insurance
lowered market capital requirements by guaranteeing depositors repayment even if their bank failed.
The original explicit deposit-insurance premium was fixed by law at one-twelfth of 1 percent of
domestic deposits. Among other regulatory changes of the time, restrictions were placed on the
interest rates that banks could pay on deposits. This provided an additional subsidy to banks that also
made uninsured bank deposits safer, reducing further market capital requirements (see Berger et al.
1995).
2. The ''safety net" refers to all government actions designed to enhance the safety and soundness of
the banking system other than regulatory and enforcement of capital regulation, such as deposit
insurance.
3. See Merton (1977) and Crouhy and Galai (1986, 1991).

Page 92
4. It should be noted that both the Bank of England and SFA (now, the FSA) in the United Kingdom
have had model-based market risk capital charges for many years under the Amsterdam Accord.
5. The precise definition of these capital ratios under the 1988 Accord and the new 1996 Amendment
is discussed in Sections 3.1–3.5.
6. Ironically, had these rules been effective in 1994, Barings could not have built these huge futures
positions on the SIMEX and OSE, and its failure could have been avoided. Indeed, when Barings
collapsed in February 1995, Barings' exposures on the SIMEX and OSE were 40 percent and 73
percent of its capital, respectively (cf. Rawnsley 1995).
7. Chapter 12 offers a detailed presentation of credit risk enhancement techniques and the credit
derivatives that are available to mitigate credit risk.
8. The G-10 is composed of Belgium, Canada, France, Germany, Italy, Japan, the Netherlands,
Sweden, the United Kingdom, and the United States. On the Basle Committee sit senior officials of
the central banks and supervisory authorities from the G-10 as well as officials from Switzerland and
Luxembourg. The Accord was fully implemented in 1993 in the 12 ratifying countries. This Accord
is also known as "the BIS requirements" since the Basle Committee meets four times a year, usually
in Basle, Switzerland, under the patronage of the Bank for International Settlements (BIS). BIS is
used in the text as a generic term to represent indifferently the Basle Committee and the regulatory
authorities that supervise the banks in the member countries.
9. Default correlation increases with concentration. To make a simple analogy, when one house is
burning, the house next door is more likely to be set on fire than a house situated further away.
10. Netting is, de facto, in effect in many derivatives transactions, such as interest rate swaps where
only interest payments are exchanged and not the principal amounts.
11. According to the banks' regulators, however, the Accord takes account of these risks by setting a
minimum capital ratio that acts as a buffer to cover not only credit risk but also all other risks. This
argument is far from convincing.
12. See, e.g., Chew (1996).
13. Tier 3 capital, however, cannot support capital requirements for the banking book.
14. See also Section 5.1.3.
15. Cf. Basle (1996). In 1993, the European Commission adopted the Capital Adequacy Directive
(CAD), imposing uniform capital

Page 93
requirements for securities trading books of banks and securities houses chartered within
the European Community. In many ways, the CAD follows the new BIS guidelines (cf.
Elderfield 1995). It has been effective since January 1996, two years before the BIS
market risk proposal was applied, giving banks in the rest of the G-10 countries a
comparative advantage over their European counterparts. It should be noted that in North
America, large securities houses such as Goldman Sachs, Salomon Brothers, and Merrill
Lynch, which are not regulated by the Office of the Controller of the Currency (OCC), the
Federal Reserve System, or the Federal Deposit Insurance Company (FDIC), in the United
States, or the Office of the Superintendent of the Financial Institutions (OSFI) in Canada,
will not have to satisfy any such minimum capital adequacy requirements. Instead, they
are subject to the rules imposed by the Securities and Exchange Commission (SEC) in the
United States, which are less stringent. However, trading opportunities and the profitability
of those securities houses depend heavily on their credit ratings. It is probable that rating
agencies such as Moody's and Standard and Poor's will play an active role in promoting
similar standards among securities houses, and will condition their attribution of top
ratings to the implementation of best-practice risk management.
16. Cf. Basle (1995).
17. By "trading book" we mean the bank's proprietary positions in financial instruments,
whether on or off the balance sheet, which are intentionally held for short-term trading, and/or
which are taken on by the bank with the intention of making profit from short-term changes in
prices, rates, and volatilities. All trading book positions must be marked-to-market or marked-
to-model every day. For market risk capital purposes, an institution may include in its measure
of general market risk certain non-trading-book instruments that it deliberately uses to hedge
trading positions.
18. In fact, the real issue at stake here is not whether to lower the amount of capital that is
required, but how to allocate the right amount of capital. The current regime charges too much
capital to investment-grade facilities and not enough to the most risky facilities. It has
encouraged massive regulatory arbitrage (see Section 5 of this chapter).
19. The new BIS proposal contemplates generalizing the system adopted by the FSA in the
United Kingdom to all the G-10 countries. See Section 5.1.2 on the supervisory review
process.
20. A revolver is a facility that allows a bank customer to borrow and repay a loan at will
within a certain period of time.

Page 94
21. Robert Merton and Myron Scholes received the award. Fischer Black died in 1996; the Nobel
Prize is not awarded posthumously.
22. See McDonough (1998).
23. There is an obvious contradiction between maintaining the current level of capital and reducing
the divergence between regulatory and economic capital. The objective should be rather to make sure
that banks carry the right amount of capital for the risks they incur. If banks reduce the amount of risk
they undertake, we would expect a lower regulatory capital to apply to them. If banks increase their
overall risk level, regulatory capital should also be set at a higher level.
24. According to the Basle Committee the proposal only applies to internationally active banks on a
fully consolidated basis, including holding companies that are parents of banking groups. This
proposal could be costly to Japanese banks which, unlike U.S. banks, are not accustomed to having
capital rules that apply at the holding company as well as at the bank level. However, in some
instances some banking groups are registered not as banks but as entities such as insurance companies
or investment houses. Firms such as Merrill Lynch, Morgan Stanley, AIG, or Prudential might decide,
for example, to engage more fully in banking activities.
Smaller banks that do not fall under the "internationally active" designation to which Basle rules
apply may seek an exemption from the new framework. There is obviously the risk that a two-tier
system will develop over time.
25. See Chapters 8, 9, and 10.
26. In order to be eligible for lower than 100 percent weighting, a sovereign would have to subscribe
to the IMF's Special Data Dissemination Standard (SDDS).
27. Chapter 8 describes the methodology of CreditVaR, the internal credit value-at-risk model
implemented at CIBC.
28. See, e.g., ISDA (2000, p. 26)'s "Index Approach." ISDA, 2000, "A New Capital Adequacy
Framework: Comments on a Consultative Paper Issued by the Basle Committee on Banking
Supervision in June 1999," February.
29. ISDA (the International Swaps and Derivatives Association) and IIF (the Institute of International
Finance) formed a joint working group in 1998 to explore how the various industry-sponsored credit
VaR models (CreditMetrics, KMV, CreditRisk+, and various proprietary models) perform for
different portfolios: corporate bonds and loans,

Page 95
middle markets, emerging market bonds, mortgages, and retail credits. Results from this study are
reported in Chapter 11.
30. Market VaR models are backtested by comparing the daily profit and loss (P&L) of the trading
account to the daily VaR (see Chapter 5). Each year 250 observations are produced to assess the
validity of the model. Since most credit risk statistics are produced on an annual basis and credit risk
models typically employ a one-year horizon, credit VaR produced on one day needs to be compared
with the P&L over the next 365 days.
31. The analogy with fixed-income derivative models for OTC products is especially relevant here.
No secondary market for exotic customized structures exists. While the positions are marked-to-
model every day using complex analytic algorithms, there is no easy way to backtest these models.
The first step in the model approval process consists of making sure that the model is theoretically
sound and consistent with finance theory. For example, a simple Black–Scholes type of model to
value a two-year option on a three-year bond would immediately be rejected. Deciding between, say,
a one-factor or a multifactor interest rate model is an act of faith since both models may be perfectly
sound. The final choice should be based on the judgement and experience of the trader and the
financial engineer. However, once the model has been chosen, it is essential to validate its calibration
and the key input parameters.
32. See the next subsection on credit risk mitigation techniques, as well as Chapter 11.
33. The proposed framework is similar to the "prompt corrective action" in the Federal Deposit
Insurance Corporation Improvement Act of 1991 under which supervisors would intervene as a
bank's capital position slipped. See Jones and King (1995).
34. As we noted earlier, most banks already hold capital beyond the minimum risk-based capital
ratios (see Table 2.7). However, regulators may impose more regulatory capital than the minimum
requirement for large banks given the large systemic effect that may result from their failure.
35. Most of these institutions participated in the G-12 recommendations.
36. The G-12 recommendations elaborate greatly on the guidelines released by BIS in January 1999
to enhance banks' risk management practices in respect of highly leveraged institutions. See the two
documents: "Banks' Interactions with Highly leveraged Institutions" and "Sound Practices for Banks'
Interactions with

Page 96
Highly leveraged Institutions." See also the "Report of The President's Working Group on
Financial Markets: Hedge Funds, Leverage, and the Lessons of Long Term Capital Management."
37. It is interesting to note that the general theme of enhanced transparency and better disclosure is
common to the proposals issued by BIS and industry-sponsored groups.
38. See also Gibson (1999) who proposes a comprehensive framework for the disclosure of market
and credit risks to all market participants (rather than just to supervisory authorities). Such a policy
should benefit firms by reducing their cost of capital, since it reduces moral hazard and adverse
selection problems.

Page 97
Chapter 3—
Structuring and Managing the Risk Management Function in a Bank
1—
Introduction
If they are to measure, price, and control risk in a comprehensive manner, financial institutions must
establish appropriate firm-wide policies, and develop relevant firm-wide risk methodologies that are
coupled to a firm-wide risk management infrastructure. This chapter provides an integrated
framework for just such an approach to risk management, in the context of best-practice risk
management.
An important component of integrated risk management is the measurement and management of all
the firm's risk in terms of a common measurement unit and strategy. The risks that need to be covered
include trading market risk, corporate treasury gap market risk, liquidity risk, credit risk in the trading
book, credit risk in the banking book, and operational risk. (Section 5 of this chapter offers a
treatment of gap market risk and liquidity risk; other chapters of this book offer in-depth discussions
of credit, market, and operational risk.)
Risk integration offers all sorts of benefits. For example, financial institutions can combine the
measurement of trading market risk and gap market risk to ensure that market risk is covered
completely and consistently. It also allows institutions to rationalize their approach to market and
credit risk measurement. For example, trading market risk and credit risk can be assessed from the

Page 98
Figure 3.1
Steps Toward Integrated Risk Management
same market value distribution, taken at selected points in time over the life of a transaction.
What do we mean by best-practice risk management? Best-practice risk management philosophy can
be envisioned along the arrow of Figure 3.1. The ultimate objective is to manage risks actively in a
portfolio context. First, a limit management process is needed to help identify and select those risks
that the firm is willing to take. A process to monitor closely the risks that are retained in the books is
also required.
Financial institutions need to implement best-practice risk analysis and risk measurement to capture
accurately their risk exposures. This is the purpose of the market and credit value-at-risk (VaR)
models we discuss in later chapters, which should be implemented for all trading businesses. Risk
analysis should be complemented by stress testing and scenario analysis to assess the extent of
potential losses during exceptional market crises.

Page 99
Best practice is also about the management of day-to-day risk communication. For example, risk
managers should discuss their risk analysis with senior trading management in a daily trading-room
risk conference; the discussion should be prior to the opening of trading and might take around 30
minutes. Automated daily exception reports should be distributed at the meeting. Risk management
should also conduct a weekly (say, two-hour) risk meeting with their internal business partners in
order to review major risk-related business issues.
The measurement of risk-adjusted return on capital (RAROC) is a particularly important part of an
integrated risk management framework, and is the foundation of performance measurement. This
measurement allows a bank to manage all its businesses in terms of their risk-adjusted return through
the assignment of reserves and economic capital, as we discuss in more detail in Chapter 14. Each
time a new transaction is considered, the bank can assess its marginal impact on economic capital,
and make sure that the pricing is consistent with its target adjusted return on capital, also known as
the hurdle rate.
Then, all the pieces are in place to ensure optimal risk pricing and active portfolio management.
2—
Organizing the Risk Management Function:
Three-Pillar Framework
Today, it is relatively unusual to find sophisticated risk literate organizations with a decentralized risk
management structure, where risk is managed to a minimum standard and risk assessment remains
under the direct control of risk takers.
Firms understand that they need to establish a risk management function that is independent of direct
risk takers. But at many firms senior managers need to encourage risk takers and risk managers to
accelerate their efforts toward establishing a more uniform and sophisticated risk management
framework.
Such a framework can be benchmarked in terms of policies, methodologies, and infrastructure
(Figure 3.2). The bank needs to develop best-practice policies (e.g., price risk authorities for the
trading book, credit risk authorities for the loan book), best-practice methodologies (e.g., market and
credit value-at-risk, stress

Page 100
Figure 3.2
Risk Management Framework
testing) that protect against losses while supporting a profitable business, and also a best-practice
infrastructure.
The independent first-class active management of risk, as shown in the center of Figure 3.2, includes
the capability to attribute capital, to appropriately price risk, and to actively manage the portfolio of
residual risks.
2.1—
Best-Practice Policies
Risk tolerance must be expressed in terms that are consistent with the bank's business strategy (Figure
3.3). The business strategy should express the objectives of the financial institution in terms of risk/
return targets. This should lead to setting risk limits, or tolerances, for the organization as a whole,
and for its major activities.
2.1.1—
Market Risk Policy
Business and risk managers should establish a policy that explicitly states their risk policy in terms of
a statistically defined potential or "worst case" loss: dealers and loan officers require a

Page 101
Figure 3.3
Best-Practice Policies
policy that states how much money can be put at risk. To this end, most major financial institutions
are moving toward a value-at-risk (VaR) framework, which calculates risk in terms of a probabilistic
worst-case loss.
A best-practice market risk policy should state the statistically defined worst-case loss in a way that
considers the probability of both parallel and nonparallel shifts in the yield curve (see Chapter 5). The
policy should also define the worst-case loss in terms of a sufficiently low level of probability, say, 1
percent.
Management should decide how to allocate capital and risk units across activities and divisions in the
institution in order to achieve their goals, while controlling exposure to market risk. The greater the
market risk, the higher the expected rate of return that the bank can expect. The question is, how
much risk exposure can the bank afford? Management should also set the authorities for assuming
market risks, and specify the nature of the market risks to which the institution should be exposed.
For example, a local or regional bank might decide to limit its exposure mainly to interest

Page 102
rate and local credit risks, while minimizing its exposure to currency risks.
2.1.2—
Credit Risk Policy
Every bank must determine a credit risk policy: how much credit to supply, for what duration, for
which type of clients, and so on. Apparent profitability is only one consideration, the second being
the risk of the loan. Therefore, bank policy should specify the extent of diversification, limits on size,
and more. Banks need to tie their tolerance for risk and associated economic capital into their desired
credit rating. For example, a desired AAA rating would require that more economic capital be
charged to business units than for a AA rating.
Some of the credit risks can be diversified away, and others should be priced. Management should
specify its tolerance to credit risk, and limit the loan losses (in probability terms). Authorities for
approving credit by size and by risk exposure should be set. A reporting system to track exposures to
credit risk is required, coupled with a routine for updating information about creditors.
2.1.3—
Operational Risk Policy
Operational risks are inherent in all banking and business activities (see also Chapter 13). These are
the risks stemming from human errors, computer failures, employing large amounts of data for
estimation purposes, and implementing pricing and valuation models. Management should decide
which operational risks it should insure, and which it should manage. Assigning responsibilities is of
utmost importance, but it cannot be effective without first-class control procedures.
All trading authorities should include a full review of operational risks. It is particularly important to
set policies that establish how to
• Review the introduction of all new products.
• Evaluate (or ''vet") all the pricing models that are used to value positions—a duty that must be
undertaken by an independent risk management function.
Operational risk management is not only about "model risk," but also about the administrative
management of the trading process (Chapters 13 and 15). It was the ability of a trader at Barings to act
without authority and detection that resulted in such large

Page 103
losses. The Bank of England report on Barings revealed some general operational risk lessons.
First, management teams have the duty to understand fully the businesses they manage. Second,
responsibility for each business activity has to be clearly established and communicated. Third,
relevant internal controls, including independent risk management, must be established for all
business activities. Fourth, top management and the audit committee must ensure that significant
weaknesses are resolved quickly.
2.2—
Best-Practice Methodologies
Going forward, banks with sophisticated risk measurement systems will be able to use their own
internal risk methodology to calculate the required amount of market risk regulatory capital in lieu of
the more onerous standardized regulatory approach.
For example, as we mentioned above, a bank might develop a policy that conservatively defines a
statistically "worst case" loss in "normal markets" as an amount such that there is less than, say, a 1
percent probability of losing more than the worst case amount in one day. In other words, the bank
might expect to exceed the statistically defined worst case loss in one out of every 100 business days.
The best-practice methodologies illustrated in Figure 3.4 refer to the application of "appropriate"
analytic models to measure market risk, credit risk, operational risk, and so on. The objective is not
solely to measure risk, but also to ensure that the pricing and valuation methodologies are
appropriate.
As pointed out in Chapter 2, the Group of Thirty (G-30) recommends that dealers should value
derivatives at market prices. Further, it recommends that risk managers should quantify market and
credit risk using a VaR framework. Specifically, the G-30 recommends that credit risk exposure
should take account of both current and potential exposure.
Finally, measurement tools should be developed to ensure that the bank's positions are on the
efficient frontier of the trade-off between risk and reward. To this end, implementing a RAROC
approach is particularly important. Simply put, what you can't measure well, you can't manage or
price well (see also Chapter 14).

Page 104
Figure 3.4
Best-Practice Methodologies
2.2.1—
Risk Measurement Methodology
A simple example will serve to illustrate what we mean by a statistically defined worst case market
risk policy for a bond, e.g., a short position in a five-year Treasury note. Typical old-style risk
methodologies (i.e., duration calculations) posit a simple parallel shift in the yield curve. One might
calculate the amount at risk by assuming that every point along the yield curve shifts downwards in a
parallel fashion by some arbitrary amount (say, one basis point, two basis points, or 25 bp 1 ).
For example, assume the five-year yield to maturity is 6.75 percent. One might arbitrarily assume that
the five-year yield to maturity declines overnight by 25 bp from 6.75 percent to 6.50 percent, and also
that every point on the yield curve declines in parallel by the same amount, i.e., 25 bp. This is clearly
a simplistic approach since the yield curve rarely shifts in a parallel fashion.

Page 105
A more realistic approach is to calculate a statistically defined worst case risk by taking into account
the more complicated non-parallel shifts in the yield curve, i.e, the yield curve might flatten, steepen,
or invert.
If interest rates were to rise, then the portfolio would gain in value. The value of the portfolio at the
current yield of 6.75 percent is $43.764 million. Assume further that if interest rates fall by one basis
point from 6.75 percent to 6.74 percent, then the value of the short position falls to $43.744 million.
Accordingly, the sensitivity of the portfolio is the difference between the value at 6.75 percent and
6.74 percent, which represents a loss of $20,000 for the short position.
However, more sophisticated systems would capture the effects of level and shape changes in the
curve. A full VaR measurement methodology encompasses more intricate types of risk, e.g., credit
spreads or vega-related option risk. This approach permits a consistent measurement of market risk
across all business units. 2
Senior management should adopt a credit risk measurement policy which calls for measuring credit
risk for the loan book and off-balance-sheet derivative products according to an analytic approach
that is consistent with the approach implemented for market risk.
2.2.2—
Pricing and Valuation Methodologies
It is particularly vital that banks develop appropriate techniques to differentiate between transactions
where prices are transparent, and those where price discovery is more limited. For example, price
discovery can be limited in the case of long tenor or highly structured derivative transactions (e.g., a
10-year option on a 20-year swap). These instruments can only be valued using assumption-driven
methodologies, and thus require the use of mark-to-model risk control techniques.
The G-30 recommends that one should take the mid-market price of the trade, less the sum of the
expected credit loss and the future administrative costs, when valuing a perfectly matched derivative
transaction. Banks need to ask themselves whether their approach to estimating the expected credit
loss is "reasonable." The G-30 also suggests additional adjustments for close-out costs—i.e., the cost
of eliminating market risk at any given point—as well as for investing and funding costs.

Page 106
2.2.3—
Accounting for Portfolio Effects
Pricing risk at the transaction level, without considering portfolio effects across an entire
organization, tends to "price in" too much risk because it does not take into account portfolio effects.
On the other hand, pricing in risk at the portfolio level is complicated.
If portfolio effects are taken into account, then one can calculate the required economic capital for the
entire organization. Economic capital is attributed as a function of risk, and is sometimes referred to
as risk capital. The economic capital required at higher organization levels is less than the sum of the
economic capital across organizational units required at lower levels. Economic capital should be
compared across organizational levels and within each level (e.g., across products). A portfolio-based
risk measurement system that incorporates correlations between positions can assist an organization
in understanding its risk profile not only by counterparty, but for the organization as a whole.
A well-designed portfolio risk measurement approach enables one "to slice and dice" risk vertically
and horizontally across an organization to facilitate the pricing of risk.
2.3—
Best-Practice Infrastructure
How important is risk infrastructure? Well, imagine a situation in which policies and methodology
have been developed but where there is no infrastructure to make them work.
The first and most important component of infrastructure in a financial services company is people
(Figure 3.5). Given the right environment and support, it is people who make everything else happen.
Best-practice risk measurement cannot be derived solely from complex analytical approaches:
judgment will always be a significant input.
Likewise, ensuring the integrity of data provides an important competitive advantage, as data are
translated into risk management information for both transaction makers and policy makers. Finally,
a key goal, critical to the successful management of risk, is to integrate risk management operations
and technology.
Increasingly, financial institutions are using sophisticated computer technology to accelerate their
efforts to establish best-practice risk management. The most important effects of this ac-

Page 107
Figure 3.5
Best-Practice Infrastructure
celeration are increasing competition, shortened time horizons for the development and distribution
of financial products, and the need to maintain a rational and consistent risk management approach.
Typically, firms are faced with the problem of fragmentation in their existing systems. The systems
cannot easily communicate with each other—the "islands of automation" problem.
Many risk management systems are developed to perform unique functions, but in some cases the
functions overlap. This causes redundancy, expensive processing, and increased costs, as each system
must be supported separately. However, new technologies facilitate the development of firm-wide
risk management support applications. The implementation of an integrated risk management system
should enable a firm to maintain a competitive advantage by allowing the firm to monitor and
manage all of its risk on a global basis.

Page 108
2.4—
Integrated Goal-Congruent Risk Management Process
An integrated goal-congruent risk management process that puts all the elements together, as
illustrated in Figure 3.2, is the key that opens the door to an optimal firm-wide management of risk.
"Integrated" refers to the need to avoid a fragmented approach to risk management. Risk management
is only as strong as the weakest link. "Goal-congruent" refers to the need to ensure that policies and
methodologies are consistent with each other. One goal is to have an apple-to-apple risk measurement
scheme so that the bank can compare risk across all products and aggregate risk at any level.
Advanced analytical techniques combined with sophisticated computer technology open up new
value-added possibilities, as illustrated in Figure 3.6, for financial risk management.
The end product is a best-practice management of risk with actions that are consistent with business
strategy. This is a "one firm, one view" approach, which also recognizes the specific risk dynamics of
each business.
Figure 3.6
Opening up New Value-Added Possibilities

Page 109
3—
Data and Technological Infrastructure
3.1—
Introduction
The key features of an effective risk management system are shown in Figure 3.7. An effective risk
management system needs to be able to generate the necessary risk management information on all
risks, perform specific analytical functions, and permit multi-tasking. Clearly, the bank also needs
well-designed back-up / retrieval capabilities. The system should allow for easy integration of new
applications and platforms, but balance this flexibility with the need for management control.
The panels in Figure 3.8, which build on the features introduced in Figure 3.7, imply that having a
first-class risk management system is a necessary condition for an optimal return-versus-risk profile.
Figure 3.7
Key Features of a Best-Practice Risk Management System

Page 110
Figure 3.8
Enhancing Return Versus Risk
3.2—
Information Technology Architecture
The risk management system needs to be supported by an information technology (IT) architecture
that is employed in all of the company's information processing. The IT architecture is essentially a
set of standards and guidelines (input from business principles) that should be adhered to by staff
when they make technological decisions.
The logic behind developing an IT architecture in terms of standards and guidelines is simple. If
business principles drive the organizational requirements for technology (and if standards and
guidelines are developed in support of the business principles), then it follows that technological
investments that adhere to these standards and guidelines will automatically support the business
principles. The IT architecture can be thought of as a collection of sub-architectures that support each
entity within the firm.
Banks have many business units, which are engaged in different activities and support different
products. The design of the IT infrastructure should optimize the exchange of information between
each entity within the firm. All should be operating within a unified IT framework.

Page 111
An "application architecture" establishes the technical, functional, and operational characteristics of
application systems (their construction and use). A "data architecture" (e.g., object-oriented) deals
with the establishment of an environment in which all information can be accessed and understood by
any associate of the firm. The ''organization architecture" deals with the responsibilities and
interrelationships necessary to ensure the comprehensive information interchange between parties.
A complete risk management system approach is not simply an aggregate of applications, data, and
organization; instead, it is born out of an IT vision. The IT design (Figure 3.9) clearly needs to take
into account the means by which key risk management information is gathered from the various
internal and external systems into a risk data warehouse. A key task is to organize the nec-
Figure 3.9
Risk Data Warehousing

Page 112
essary risk management data (transmitted to the risk management system from multiple legacy
systems) into a common format (data dictionary).
Furthermore, IT planning needs to take account of how key risk management information might
change over time. The information might be static (e.g., contractual details of a transaction such as
the coupon of a corporate bond) or dynamic (e.g., market information such as daily closing prices).
The IT platform and operating system should be designed such that they do not place constraints on
managers trying to obtain risk management data.
Attempting to calculate and manage risk on a global basis requires the centralized control of
algorithms and immediate access to large amounts of data. Risk management data include both
historical statistics and current risk characteristics, for each transaction in every portfolio.
Bank trading units are typically dispersed among markets in multiple time zones. To centralize the
risk calculation, and provide immediate access to data, an organization must develop its IT
architecture from best-in-class database and communication technologies.
A distributed database approach is often used to distribute risk management data. Distributed
databases promote the distribution of data and decision making to regional sites (e.g., New York,
Toronto, London, Singapore, Hong Kong, and Tokyo). A distributed database enables an
organization to store data on the network wherever it is most economical, rather than on each remote
database server. An overseas office can request information on any financial instrument from other
sites. Distributed data technologies offer a low-cost solution to the problem of providing risk
management data for global risk-related decision making. Figure 3.10 illustrates a distributed
database technology with interconnected servers.
3.3—
Tiered Risk Management Systems
Trading institutions should select a suitable three-tiered risk management system to integrate their
front office, middle office, and back office. The middle office handles functions such as risk
management, monitoring key trades, pricing deals, etc. The back office

Page 113
Figure 3.10
Distributed Database Technology with Interconnected
Servers
performs routine functions such as recording the amount of interest paid, maintaining tax accounting
information, performing regulatory reporting, etc. New trading platform technologies are being
engineered and constructed to integrate the front and back offices with the middle office.
Managers in major institutions need to ensure that their enterprise-wide risk management computing
is capable of running on centrally located hardware (Figure 3.11a). The risk management database
(e.g., a UNIX-based database) must be able to store extracted data and to allow for interactive
unscheduled access or "interrupt functionality" (Figure 3.11b).
Also, the institution needs to establish an effective and integrated workgroup computing environment
(Figure 3.11c). The workgroup computing environment supports risk management end-users, policy
makers, and application developers.
Finally, the bank needs to ensure that the corporate networks connect all three risk management tiers
(Figure 3.12), so that risk management data can be exchanged. The corporate network connects all the
tiers by allowing software and data to be easily transferred through the network. Multiple users at
different organizational levels should have easy access to risk software applications,

Page 114
Figure 3.11a
Enterprise-Wide Centralized Risk Management
Figure 3.11b
Risk Data Warehouse

Figure 3.11c
Work Group Computing Environment

Page 115
Figure 3.12
Three Tiers to an Integrated Risk Management System
data, and reports. Advanced risk management software—e.g., object-oriented programming
languages (such as C++)—facilitates ambitious integration projects.
The risk management system should be designed to support the transport and integration of risk
information from a variety of technology platforms, as well as from multiple internal and external
legacy systems around the world. The risk management infrastructure is similar to a highway system
in that it enables these legacy systems to transport information without the bank having to
continuously build new roads for its data.
The bank's risk data warehouse should be populated daily with transaction and market information.
The transaction information should also be reconciled daily to ensure that market risk is reported
accurately. The risk data warehouse should also store a time series of market data in its financial
database.
Risk reports should be generated daily by an analytic engine that has been designed by the bank's risk
management function. The analytic engine should be built with a flexible architecture to
accommodate advanced risk measures. As a whole the system should be able to: (1) develop and
distribute financial instruments

Page 116
quickly; (2) aggregate risks across the institution; and (3) supply transaction personnel with
information on limits, as well as RAROC expectations.
A major challenge is to integrate existing risk management systems with new platform technologies.
Financial institutions will likely have to make substantial and significant investments in their
computer technology in order to provide their clients, risk takers, and risk managers with the speed
and analytics necessary to monitor and perform risk management.
4—
Risk Authorities and Risk Control
We begin this section with the issue of risk management roles and responsibilities. Second, we
describe standards for risk authorities and how these risk authorities should be monitored. Third, we
provide standards for limit design. Fourth, we provide standards for risk monitoring. Finally, we
briefly discuss the role of a bank's audit function.
4.1—
Roles and Responsibilities
Market risk roles and responsibilities should be understood at all levels of the bank. An independent
market risk management function should develop risk policy, and monitor adherence to such policy.
A knowledgeable internal audit function should provide an in-depth assessment of internal risk
management controls, including controls over the risk management function.
Best-practice corporate governance demands that a subcommittee of the board of directors (say, a risk
management and conduct review committee) reviews and approves risk management policies at least
once a year. A senior operating policy committee (say, an asset/liability management committee)
should be responsible for determining the extent of financial risk to be accepted by the bank as a
whole.
The asset/liability management committee (ALCO) is typically responsible for establishing,
documenting, and enforcing all polices that involve market risk, such as liquidity, interest rate, and
foreign exchange risk. ALCO is also responsible for the delegation of market risk limits to the
president and chief risk officer (CRO)

Page 117
of the bank. ALCO should also ensure that the bank's infrastructure can support the bank's market
risk management objectives.
The chief risk officer is responsible for risk management strategy, policies, methodologies, and
overall governance. ALCO delegates to the chief risk officer the authority to make day-to-day
decisions on its behalf, including the authority to extend business unit mandates beyond their annual
renewal date until it is convenient for ALCO to review them, and to approve excesses of limits
provided that these do not breach overall risk limits approved by the board (i.e., the risk management
and conduct review committee of the board).
A business-level risk committee should be responsible for ensuring that the desired risk/reward trade-
offs are successfully managed. The committee should manage design issues that set out how risk will
be managed, reflecting the agreed relationship between the business and the bank's risk management
function. The committee should also approve policies applicable to the appropriate measurement and
management of risk, and provide a detailed review of risk limits for trading and credit authorities.
Managers are necessarily dependent upon each other when they try to manage risk in a bank (Figure
3.13). Senior management approves business plans and targets, sets risk tolerances, establishes
policy, and ensures that performance targets are met. Trading-room managers establish and manage
risk exposures. Trading-room managers also ensure timely, accurate, and complete deal capture and
sign off on the official profit and loss (P&L) statement.
The bank's operations function independently books trades, settles trades, and reconciles front- and
back-office positions. Operations staff also prepare the daily P&L report. Operations staff are also
responsible for providing an independent mark-to-market of the bank's positions, and support the
operational needs of the various businesses.
The finance function develops valuation and finance policy, and ensures the integrity of P&L—
including reviews of any independent valuation processes. Finance also manages the business
planning process, and supports the financial needs of the various businesses.
Meanwhile, the risk management function develops risk policies, monitors compliance to limits,
manages the ALCO process, vets models and spreadsheets, and provides an independent view

Page 118
Figure 3.13
Interdependence for Managing Risk
on risk. The function also supports the risk management needs of the various businesses.
4.2—
Standards for Risk Authorities
It is best practice for institutions to write down the policies and procedures that govern their trading
activities. These policies

Page 119
include how a bank approves new products as well as how it establishes market risk limits. The
standards should cover the nature of any formal reviews of market risk exposures, as well as the
analytic methodology used to calculate the bank's market risk exposures. The standards should also
establish procedures for approving limit exceptions.
4.2.1—
Business Unit Mandate
The process for developing and renewing authorities should be explicit. For example, business unit
mandates should expire one year after they are approved by ALCO. The senior risk officer may
approve an extension of an authority beyond one year, to accommodate ALCO's schedule.
A balance must be struck between ensuring that a business has the limits set high enough to allow it
to meet its business goals, and the maintenance of overall risk standards (including ensuring that
limits can be properly monitored). Key infrastructure and corporate governance groups must be
consulted when preparing a business unit's mandate.
The format for obtaining approval of a business unit mandate should be standardized. First, the
manager seeking approval should provide an overview and restate the key decisions that need to be
taken (as requested by the senior policy committee).
Second, the manager should bring everyone up to date about the business, e.g., key achievements,
risk profile, and a description of any new products (or activities) that may affect the risk profile.
Third, the manager should outline future initiatives.
Fourth, proposed risk limits should be put forward. The report should note the historical degree of
use of any current limits, as well as current and proposed limits. It should analyze the impact of any
full use of limits on liquidity and capital.
Fifth, the report should describe the operational risks that the business unit is exposed to. This would
include the impact of any finance, legal, compliance, and tax issues.
4.2.2—
Delegation Process for Risk Authorities
The risk management and conduct review committee of the board should approve the bank's risk
appetite each year and delegate authority to the chief executive officer of the bank as chair of ALCO.
ALCO should approve each business unit mandate (say, annually).

Page 120
ALCO also approves the impact of each mandate in terms of the market risk appetite of the bank and, in
turn, delegates market risk authority to a business-driven risk committee.
The risk committee provides a detailed review and approval (say, annually) of each business unit mandate.
The committee also approves the impact of each mandate in terms of the respective risk limits, and
delegates these limits to a chief risk officer. The chief risk officer is responsible for independently
monitoring the limits—and may well order that positions be reduced, or closed out because of concerns
about market, credit, or operational risks. The chief risk officer also delegates some responsibilities to the
head of global trading.
The head of global trading is responsible for risk and performance of all trading activities, and in turn
delegates the management of limits to the business manager. The business manager is responsible for the
risk management and performance of the business and, in turn, delegates limits to the bank's traders. This
delegation process is summarized in Figure 3.14.
Figure 3.14
Delegation Process for Market Risk Authorities

Page 121
4.3—
Standards for Limit Design
What is the best way of designing the various risk limits? Market risk should be measured using a
VaR-style risk measure that is based on a common confidence interval and on an appropriate time
horizon. Market risk limits should control the risk that arises from changes in the absolute price (or
rate), as well as changes in delta, gamma, volatility (vega), time decay (theta), basis, correlation,
discount rate (rho), and so on. Policies should also be set out regarding exposure to liquidity risk,
especially in the case of illiquid products. Banks should also include limits related to stress events
and scenario analyses, to make sure the bank can survive extreme volatility in the markets.
Institutions should employ both tier I and tier II limits. Tier I limits should include a single overall
VaR limit for each asset class (e.g., a single limit for foreign exchange products), as well as a single
overall stress test limit and a cumulative loss from peak limits.
Tier II limits should include authorized markets/currencies/instruments, and concentration limits
(e.g., by maturity, region, etc.). All risk limits should be consistent with the standards for risk limits
proposed by the risk management function, and approved by the risk committee. Limits should
balance the needs of the business to meet its financial targets with a realistic assessment of the use of
past limits. The tier I limits should generally be set at a level such that the business, in the normal
course of its activities, has exposures of about 40 percent to 60 percent of its limit (in normal
markets). Peak usage of limits, in normal markets, should generate exposures of perhaps 85 percent
of the limit.
The actual and proposed limits should be based on an evaluation of the bank's tolerance for risk, as
well as the risk management function's ability to provide timely and accurate reporting on relevant
risks, and the historical usage of risk limits.
A consistent limit structure helps a bank to consolidate risk across its various trading floors. With a
common language of risk, tier II limits become fungible across business lines. Nevertheless, such
transfers would require the joint approval of the head of trading and the chief risk officer.

Page 122
4.4—
Standards for Monitoring Risk
How should a bank monitor its market risk limits? Firstly, all positions should be marked-to-market
daily. All the assumptions used in models to price transactions and to value positions should be
independently verified. Daily profit and loss statements should be prepared by units that are
independent of traders, and provided to (nontrading) senior management.
There should be timely and meaningful reports to measure compliance to policy and to trading limits.
There should be a timely escalation procedure for any limit exceptions or transgressions; i.e., it
should be clear what a manager must do if his or her subordinates breach limits.
The variance between the actual volatility of the value of a portfolio, and that predicted by means of
the bank's market risk methodology, should be evaluated. Stress simulations should be executed to
determine the impact of market changes on P&L.
Data used in limit monitoring must conform to a set of standards. First, the source of data must be
independent of the front office. Second, the data need to be reconciled to the official books of the
bank in order to ensure its integrity. Third, data feeds must be consolidated. Fourth, the data format
must allow risk to be properly measured; e.g., it might employ the VaR methodology.
The bank must distinguish between data used for monitoring tier I limits—where data must be
independent of traders—and data used to supply other kinds of management information. For other
types of analysis, where timeliness is the key requirement, risk managers may be forced to use front-
office systems as the most appropriate sources. Real-time risk measurement, such as that used to
monitor intraday exposures, may simply have to be derived from front-office systems.
Business units should advise the risk management function before an excess occurs. For example,
there might be an alert when an exposure is at, say, 85 percent of the tier I or tier II limit. The chief
risk officer, jointly with the head of business, might petition ALCO for a tier I excess, in which case
the business risk committee should be notified. If risk management is advised of a planned excess,
then it should be more likely that an excess will be approved.

Page 123
Figure 3.15
Limited Excess Escalation Procedure
What happens if the limit is breached? Risk management, as illustrated in Figure 3.15, should
immediately put any excess on a daily tier I or tier II exception report, with an appropriate
explanation and a plan of action to cope with the tier I excess. The chief risk officer may authorize
the use of a reserve.
Tier I excesses must be cleared or corrected immediately. Tier II excesses should be cleared or
approved within a relatively short time frame of, say, a week.
Risk management should report all limit excesses on an exception report, which might be tabled at a
daily trading-room meeting and which should distinguish between tier I and tier II limits. No
manager should have the power to exclude excesses from the daily excess report.

Page 124
4.5—
Role of Audit
A key role of audit is to provide an independent assessment of the design and implementation of the
risk management process. This includes examining the process surrounding the building of risk
models, the adequacy and reliability of the risk management systems, and, especially, compliance
with regulatory guidelines.
4.5.1—
Scope of Work
Audit should provide overall assurance on the adequacy of the risk management processes. A key
audit objective should be to evaluate the design and conceptual soundness of both the VaR measures
(including the methodologies associated with stress testing) and the back-testing of these VaR
measures.
Audit should also evaluate the soundness of elements of the risk management information system—
the risk MIS—such as the processes used for coding and implementation of internal models. This
should include examining controls over market position data capture, as well as controls over the
parameter estimation processes.
For example, audit responsibilities often include providing assurance on the design and conceptual
soundness of the financial rates database that is used to generate parameters entered into the VaR
analytic engine. Audit also reviews the adequacy and effectiveness of the processes for monitoring
risk, the progress in plans to upgrade risk management systems, the adequacy and effectiveness of
application controls within the risk MIS, and the reliability of the vetting processes.
Audit should also examine the documentation relating to compliance with the qualitative/quantitative
criteria outlined in regulatory guidelines. Audit should comment on the reliability of the value-at-risk
reporting framework.
4.5.2—
Regulatory Expectations
Regulatory guidelines typically call for internal audit groups to review the overall risk management
process. This means addressing the adequacy of documentation, the effectiveness of the process, the
integrity of the risk management system, the integration of risk measures into daily risk management,
and so on.
Regulatory guidelines typically also call for auditors to address the approval process for vetting risk
pricing models and val-

Page 125
uation systems used by front- and back-office personnel, the validation of any significant change in
the risk measurement process, and the scope of risks captured by the risk measurement models.
Regulators also require that internal auditors examine the integrity of the management information
system and the accuracy and completeness of position data.
Audit should verify the consistency, timeliness, and reliability of data sources used to run internal
models, including the independence of such data sources. One important duty is to examine the
accuracy and appropriateness of volatility and correlation assumptions, as well as the accuracy of the
valuation and risk transformation calculations. Internal auditors should verify the accuracy of models
through an examination of the back-testing process. Finally, audit should avoid providing measures
of risk (e.g., operational risk), as their role of auditing the key precesses would be compromised.
4.5.3—
Statement of Audit Findings
If all is well from a risk management perspective, then audit should state that adequate processes
exist for providing reliable risk control and to ensure compliance with local regulatory criteria (e.g.,
the 1998 BIS Capital Accord).
For example, the audit group's conclusion might be that (1) the risk control unit is independent of the
business units; (2) the internal risk models are utilized by business management; and (3) the bank's
risk measurement model captures all material risks.
Further, if all is well then the audit group should state that adequate and effective processes exist (4)
for risk pricing models and valuation systems used by front- and back-office personnel; (5) for
documenting the risk management systems and processes; (6) for validation of any significant change
in the risk measurement process; (7) for ensuring the integrity of the risk management information
system; (8) for the position data capture (and that any positions that are not captured do not materially
affect risk reporting); (9) for the verification of the consistency, timeliness, and reliability of data
sources used to run internal models, and that the data sources are independent; (10) for ensuring the
accuracy and appropriateness of volatility and correlation assumptions; (11) for ensuring the accuracy
of the valuation and risk transformation

Page 126
calculations; and (12) for the verification of the model's accuracy through frequent back-testing.
5—
Establishing Risk Limits for Gap and Liquidity Management
Asset/liability management (ALM) can be defined as a structured decision-making process for
matching and mismatching the mix of assets and liabilities in a bank. The aim of the process is to
maximize the net worth of the bank's portfolio while assuming reasonable amounts of gap and
liquidity risk.
Simply stated, the key objectives are:
• To stabilize net interest income (accounting earnings)
• To maximize shareholder wealth (economic earnings)
• To manage liquidity
Gap market risk arises from directional risk (mismatch risk of the interest rate sensitivity of a bank's
assets and liabilities), spread risk, and any options risk embedded in the gap.
The amount of gap market risk relates to the extent to which net interest income and price changes are
a function of a change in rates. Liquidity risk refers to the risk that the bank might not be able to
generate sufficient cash flow to meet its financial obligations.
Asset/liability management involves the deliberate mismatching of a bank's assets and liabilities in
terms of their maturity and repricing characteristics. For example, instead of waiting for new
deposits, it is standard practice for banks to make long-term corporate loans by borrowing short-term
wholesale money. The idea is to add to the bank's profits while assuming a reasonable amount of
risk.
A principal source of gap market risk arises from ''riding the yield curve." For example, gap "carry
profits" can be created by carrying a bank asset "further out" on a positively sloped yield curve than
the associated bank liability. Positive gaps are created when a bank possesses more assets in a
specific maturity bucket than it possesses liabilities. A negative gap in a short-maturity bucket will
benefit from a fall in rates, while a positive gap in a short-maturity bucket will benefit from rising
rates. Gap carry profits are locked in until the first liability repricing date.

Page 127
5.1—
Gap Market Risk
Gap market risk can be viewed from two distinct perspectives: accounting and economic. The former
focuses on the impact of changing interest rates on reported net interest income. Specifically, earnings
risk in the near term can be observed through the income statement and through the quality of the
balance sheet.
The economic perspective looks at the impact of changing interest rates on the market value of a
portfolio. In other words, the focus is on the risk to the net worth of the bank that arises from all the
bank's interest-sensitive positions. Generally, the economic risk cannot be observed by monitoring
accounting flows.
In a stable interest rate environment, the accounting (or book value) perspective of a bank's position
is similar to the economic (or market value) perspective. This is because there is little movement in
the market value of the bank's positions, or its net interest income. The situation is quite different in a
volatile interest rate environment. Net interest income is at risk due to the interest rate mismatch
embedded in any gap in the bank's portfolio of positions. From an economic perspective, the capital
(i.e., market value) of the bank changes substantially as interest rates fall or rise, reflecting the present
value of expected future cashflows.
5.2—
Measuring Gap Market Risk
The techniques used to measure gap market risk range from relatively simple and static gap analysis,
through duration analysis, to sophisticated VaR-type approaches.
A static gap analysis examines the nominal amount of the tactical and strategic gaps in the bank's
overall position, and determines if these are appropriate in terms of perceived reward/risk. The
"tactical gap" typically represents the combined gap position within one year. The "strategic gap"
represents the combined gap position beyond one year. The "contractual gap" refers to the net gap
position for assets and liabilities that have defined maturity dates. It is often difficult to determine
maturity for noncontractual balances. For example, "core balances" typically refer to the stable
portion of nonmaturity balances that are projected to remain on the balance sheet of the bank for an
extended period of time.

Page 128
One can calculate gap risk management units (RMUs) in a similar way to the RMU calculation for a
trading book. For example, assume that the bank's balance-sheet position consists of a three-month
eurodollar-based liability and a six-month eurodollar-based asset (a liability-sensitive balance sheet).
Here, the risk manager can think of the gap market risk as having the equivalent market risk to that of
any hedging portfolio that might be used to hedge away the gap. For example, one might hedge the
unmatched portion of a three-month asset starting three months from the present, by buying a 3 6
forward rate agreement. Accordingly, the gap RMU of this position can be viewed as the worst case
change in value for this forward rate agreement.
5.3—
Transfer Pricing Rules for Match-Funding a Unit
Banks need to develop a best-practice transfer pricing system (TPS) in order to properly characterize
the gap market risk. A TPS allows the risk to be managed by, say, the corporate treasury function.
There is no single right answer for building a best-practice TPS. Nevertheless, certain properties of a
TPS are more optimal than others.
Specifically, the bank will need to establish transfer pricing rates (TPRs) for a variety of complex
products: indeterminate maturities (e.g., demand deposits), options features (e.g., consumer loans
with caps), basis risk (e.g., prime-based loans), etc.
A TPS should have a clear statement of purpose, e.g., "to decentralize decision making." Business
units should not, on the whole, concern themselves with funding issues. The TPS can be used to
measure the net interest contribution of a business, based on factors that are within its control and
against a single standard.
The TPS should be consistent with a financial institution's business objectives and risk management
practices. It must be credible, comprehensible, practical—and fully embraced by senior management.
Neither regulators nor practitioner working groups have provided any position papers that serve to
define a best-practice TPS. Figure 3.16 attempts to fill this gap: It is a schematic representation of the
ten commandments of transfer pricing. The commandments are also tabulated in Box 3.1.

Page 129
Figure 3.16
Schematic Representation of the Ten Commandments
Starting with the upper right-hand corner of the figure, observe that a best-practice TPS provides business
units with automatic protection from both directional risk (commandment I) and major options risk
(commandment II), but does not provide protection against credit risk or volume risk. The TPS does not
automatically provide protection against spread risk (commandment III), unless that risk is hedgeable. TPS
best practice is based on marginal pricing (commandment IV) as opposed to average pricing.
Further, a TPS should not confuse liquidity pricing issues with transfer pricing issues. In other words,
liquidity credit/charges are kept outside of the TPS (commandment V). A best-practice TPS is designed to
reflect the profitability that can be achieved by the institution (commandment VI) and is impervious to
arbitrage (commandment VII). A well-designed TPS is global in scope (commandment VIII), and is based
on the institution's specific—i.e., inclusive of country-specific dynamics—yield curve (commandment IX).

Page 130
BOX 3.1
THE TEN COMMANDMENTS OF TRANSFER PRICING
I. Units shall be protected from directional risk.
II. Units shall be protected from significant options risk.
III. Units shall not be protected from basis (spread) risk, unless the risk is hedgeable and the units pay for the hedge based on current
market rates and for an agreed volume.
IV. The transfer pricing rate (TPR) will be based on minimizing spread volatility, while striving to price at the margin.
V. The transfer pricing (TP) rules for match-funding a unit shall be determined by interest rate sensitivity.
VI. The transfer pricing system (TPS) shall reflect the profitability that can be achieved by the institution.
VII. The TPS shall be impervious to arbitrage.
VIII. The TPS shall be global in scope.
IX. The TPS shall be institution and country specific.
X. The TPR shall be determined solely by the true economics of the transaction and the TPS shall be explicit, consistent, and goal-
congruent.
Most importantly, a well-designed TPS reflects true economic values (commandment X).
The TPS should be reviewed periodically, and be consistent with other measurement systems (e.g., liquidity pricing system). Finally, a best-
practice TPS is internally consistent and should not be used to send directional signals; neither should the rules be changed in an attempt to
mitigate the sins of the past.
5.4—
Liquidity Risk Measurement
One should not confuse interest rate sensitivity with liquidity risk. Interest rate sensitivity is determined by the frequency of the repricing of
an instrument. In contrast, it is the contractual maturity of an item that determines whether it contributes to a liquidity gap.
For example, a three-year fixed-rate loan has an interest rate sensitivity of three years, and a liquidity maturity of three years.

Page 131
A variable-rate, three-year loan priced off six-month Libor has an interest rate sensitivity of six
months, and a liquidity maturity of three years.
A business unit's impact on institutional liquidity can be characterized by means of a liquidity
measurement system. This must be "directionally correct"; a liability-gathering unit should be
credited for supplying liquidity, and an asset-generating unit should be charged for using liquidity.
For example, Table 3.1 illustrates a spectrum of funding sources and indicates that a bank might
assign a higher liquidity credit for "stable funds" than for "hot funds." "Hot funds" are funds that are
supplied by depositors (e.g., dealers) and could be quickly removed from the bank in the event of a
crisis. Table 3.1 ranks the sources of funds in terms of their liquidity.
One can illustrate the key features of a best-practice liquidity quantification scheme through a
simplified version of a liquidity ranking process. The liquidity ranking process should enable the
bank to quantify credits and charges, depending on the degree to which a business unit is a net
supplier or net user of liquidity.
Liquidity can be quantified using a symmetrical scale. Such scales help managers to compute a
business unit's liquidity score more objectively, through a ranking and weighting process.
Table 3.1
Funds Source Spectrum

Page 132
A quantification scheme such as this also helps the bank to determine the amount of liquidity in the system, and to
set targets in terms of a desirable and quantifiable level of liquidity.
The liquidity rank (LR) attributed to a product is determined by multiplying the dollar amount of the product by its
rank. For example, if business unit XYZ is both a supplier and a user of liquidity, then a net liquidity calculation
needs to be made. Looking at Table 3.2, if we assume that business unit XYZ supplied $10 million of the most
stable liquidity, $3 million of the next most stable, and so on, then a total credit of 94 (10 × 5 + 4 × 3 + 3 × 6 + 2 × 5
+ 1 × 4 = 94) would be assigned.
Similarly, if we assume in our example that business unit XYZ used $10 million of the most expensive liquidity, $3
million of the next most expensive, and so on, then a total charge of -100 (4 × 1 + 8 × 2 + 6 × 3 + 3 × 4 + 10 × 5 =
100) would be assigned. The net result of the two calculations is a liquidity rank of minus $6 million.
The LR approach is simply a heuristic tool that helps managers to control the liquidity profile of their financial
institution.
TABLE 3.2
Liquidity Rank Measurement Units
Business Unit XYZ's
Net Liquidity Rank Measurement Units
Liquidity Suppliers Liquidity Users
Rank Score Amount ($MM) Rank Score Amount ($MM)
+5 $10 –1 $4
+4 $3 –2 $8
+3 $6 –3 $6
+2 $5 –4 $3
+1 $4 –5 $10
Total 94 Total –100
Net –6 (= 94 – 100)

Page 133
The next step is to charge each business unit for the liquidity risk that it generates.
6—
Conclusion:
Steps to Success
In the past, financial institutions have treated each type of risk separately. This approach has been
undermined by the increasing complexity of products, linkages between markets, and the growing
importance of portfolio effects. Today, the profitability of a financial institution depends on its ability
to price risk and to hedge its global exposure.
How can the ideas that we have introduced in this chapter be turned into reality? One of the first
steps is to tailor the vision by identifying user and business needs, and by defining objectives,
deliverables, and benefits. One must also obtain the commitment of top management, and gain
sponsorship at the board level.
Second, the bank needs to agree on its risk management policy. For example, senior management
must approve a clear notion of how the institution defines a "worst case risk."
Third, the bank needs to agree on the risk measurement methodologies, for example, how to define
risk in terms of VaR. A best-practice VaR system can be applied to gain both a defensive advantage
and an offensive advantage. Defensive advantages include providing risk control for shareholders and
senior management. Offensive advantages include utilizing VaR as a basis for capital attribution as
well as improving the bank's return-to-risk ratio. The bank can use its VaR methodology to mine the
risk management database for trade opportunities.
Next, the managers of the bank need to agree on their organizational infrastructure. How should the
risk management function be organized to best manage the bank's risks?
A key to designing an efficient organization is to ensure that the roles and responsibilities of each risk
unit are carefully spelled out and remain complementary to one another. A detailed breakout of
typical responsibilities within trading market risk, trading credit risk, and risk analytics is shown in
Figure 3.17.
Trading-Room market risk (TRMR) management and trading-room credit risk (TRCR) units have a
responsibility to work with risk analytics and risk MIS in rolling out price risk reporting systems. The

Page 134
Figure 3.17
MRM Organization
TRMR and TRCR units approve deals and monitor risks. The risk analytics unit typically develops
the mathematics required in the implementation of market VaR and credit VaR methodologies. The
analytics function also vets all the models that are developed by dealers; develops robust, accurate,
and computationally efficient models to price and hedge complex securities; and conducts research.
Each of the units gears its infrastructure to satisfy specific objectives. For example, each morning the
head of TRMR might chair a meeting of senior managers and global dealers in order to review and
debate (in light of, say, current market conditions) the previous end-of-day market risk exposures.
For the rest of the trading day, the head of TRMR would keep abreast of ongoing developments and
changes in market risk exposures—following markets and talking to traders. The head of TRMR is
likely to sit on the trading floor alongside the chief dealers.
The TRMR unit itself might well be divided into distinct, but related, groups, for example, a policy
group responsible for devel-

Page 135
oping risk management methods and standards, an operating group charged with continuously
monitoring the firm's market risk exposures, and a third group of market risk managers who cover
specific regions (e.g., Asia, Europe, North America, South America) or products (e.g., commodity
derivatives, high-yield securities). Product specialists within TRMR might provide direct risk
management support to each product manager.
Similarly, the TRCR unit infrastructure must be geared to its aims. One of these might be to shrink to
a minimum the time between an idea occurring in a trader's head to the credit approval of the trade.
Fifth, as discussed earlier in this chapter, banks need to build a first class risk MIS system.
Sixth, the bank should encourage businesses to use the risk infrastructure as both a tactical
management and strategic planning tool. Risk information is a critical component of a globally
integrated bank.
Seventh, set clear short-term and regular deliverables. For example, every three months the risk
management function might aim to roll out upgrades to the risk management system—to include
another product or another location or to encompass another legacy system. One should build one
small subset of the risk management system at a time, and enhance the system over time. (For
example, it makes no sense to attempt to build a risk management data warehouse all at once.)
Next, one needs to clearly define the ultimate aims of the risk management process. For example, one
objective might be to allocate economic capital based on risk. A key deliverable would be to
continually refine capabilities and reports.
Finally, one needs to establish a clear philosophy for the group. For example, a philosophy might call
for the risk management function to deliver solutions, be application-driven, and remain conscious of
user needs.
Notes
1. The term basis point (bp) denotes 1/100 of 1 percent, or 0.0001.
2. At CIBC we refer to Risk Management Unit, or RMU, the common unit of risk measurement
across business.

Page 137
Chapter 4—
The New BIS Capital Requirements for Financial Risks
1—
Introduction
In this chapter we compare the two alternative ways to assess market risk set out in the Bank for
International Settlements (BIS) 1998 regulatory reform described in Chapter 2. The differences
between the two methodologies strike to the heart of the modern regulation of risk management.
Furthermore, choosing between the two methodologies is a significant issue in the business strategy
of banks. As we will demonstrate, the difference in capital charges between the two approaches is so
considerable that banks subject to the ''standardized approach" may find themselves facing a severe
competitive disadvantage. Ideally, this competitive disadvantage should encourage banks to invest in
more sophisticated methodologies in order to reap the benefits of lower regulatory capital. The
"carrot and stick" approach associated with BIS 98 is one of its most powerful features.
The standardized approach, which employs constant factors determined by the BIS for various
instruments, is detailed in Section 2. The alternative approach, the "internal model approach," is
based on the proprietary models of individual banks and the probability distributions for changes in
the values of claims. Before a bank can adopt this second approach, it must gain the approval of its
regulator. The BIS sets rules and guidelines for regulators that guide the process by which regulators
award this approval. These guidelines are detailed

Page 138
in Section 3. (Readers unfamiliar with the basic tenets of value-at-risk modeling may wish to read
Chapter 5 before reading this section.)
In Section 4 the pros and cons of the two approaches are discussed and a new approach, the
"precommitment approach," is proposed. Finally, in Section 5, a numerical example is presented to
illustrate the savings in capital requirements that can arise if internal models are employed rather than
the standardized approach.
2—
The Standardized Approach
The standardized model uses a "building block" methodology. The capital charge for each risk
category, i.e., interest rates, equities, foreign exchange, and commodities, is first determined
separately. Then, the four measures are simply added together to obtain the global capital charge that
arises from the bank's market risk. In this section we present, and illustrate with simple examples, the
main thrust of the method for the four risk categories.
2.1—
Interest Rate Risk
The model encompasses all fixed-rate and floating-rate debt securities, zero-coupon instruments,
interest rate derivatives, and hybrid products such as convertible bonds. The latter are treated like
debt securities when they trade like debt securities (i.e., when their price is below par), and are
otherwise treated like equities. Simple interest rate derivatives such as futures, forward contracts,
including forward rate agreements (FRAs), and swaps are treated as if they were a combination of
short and long positions in debt contracts. (Options are treated separately and will be covered later in
this section.)
The interest risk capital charge is the sum of two components of market risk, each of which is
separately calculated. The first component, "specific risk," applies to the net holdings for each
particular instrument. The second component is related to "general market risk," and in this case the
long and short positions in different securities or derivatives can be partially offset.
2.1.1—
Specific Risk
The capital charge for specific risk is designed to protect the bank against an adverse price movement
in the price of a security that

Page 139
TABLE 4.1
Specific Risk Charge Factor for Net Debt Positions
Debt Category Remaining Maturity Capital Charge (%)
Government Any 0.00
Qualifying Six months or less 0.25
Six to 24 months1 1.00
Over two years 1.60
Other Any 8.00
1 For Canada, OSFI has set the horizon of the second bucket to 12 months instead of 24.
is due to idiosyncratic factors related to the individual issuer of the security. For this reason, offsetting
is restricted to matched positions in the same issue, including derivatives. The capital charge applies
whether the bank has a net long or net short position. Even where the issuer of two securities is the
same, but there are differences in maturity, coupon rates, call features, etc., no offsetting is allowed.
This is because a change in the credit quality of the issuer may have a different effect on the market
value of each instrument.
Table 4.1 shows the specific risk charge for various types of debt positions. The weighting factors
apply to the market value of the debt instruments, and not to their notional amount.
The "government" category in the table includes all forms of debt instrument issued by OECD central
governments, as well as non-OECD central governments provided certain conditions are satisfied. The
"qualifying" category includes debt securities issued by OECD public sector entities, regulated
securities firms of the G-10 countries plus Switzerland and Luxembourg, and other rated investment-
grade bonds. The ''other" category receives the same specific risk capital charge as would a private
sector borrower under the credit risk requirements of the 1988 Accord, i.e., 8 percent.
A specific risk charge also applies to derivative contracts in the trading book, but only when the
underlying reference of the derivative contract is subject to specific risk. For example, an interest rate
swap based on LIBOR is not subject to a specific risk charge, while an option on a corporate bond is
subject to the charge. (Note that all over-the-counter derivative contracts are subject to a counter-

Page 140
party credit risk charge arising from the direct counterparty to the contract. The capital charge is derived
according to the guidelines of the 1988 Accord, even where a specific risk charge is required.)
2.1.2—
General Market Risk
Capital requirements for general market risk are designed to capture the risk of loss arising from changes in
market interest rates. Banks can choose between two methods, the "maturity" method and the "duration"
method. The duration method is simply a variant of the maturity method, and in this chapter we will describe
only the former. 1
The maturity method uses a "maturity ladder," i.e., a series of "maturity bands" that are divided into
"maturity zones" according to the rule given in Table 4.2. These maturity bands and zones are chosen to take
into account differences in price sensitivities and
TABLE 4.2
Maturity Bands and Risk Weights
Assumed Changes in
Yield (in Percentage Risk Weights
Zone Coupon 3% or More Coupon Less Than 3% Points) (Sensitivities)
1 1 month or less 1 month or less 1.00 0.00%
1 to 3 months 1 to 3 months 1.00 0.20%
3 to 6 months 3 to 6 months 1.00 0.40%
6 to 12 months 6 to 12 months 1.00 0.70%
2 1 to 2 years to 1.9 years 0.90 1.25%
2 to 3 years to 2.8 years 0.80 1.75%
3 to 4 years 2.8 to 3.6 years 0.75 2.25%
3 4 to 5 years to 4.3 years 0.75 2.75%
5 to 7 years to 5.7 years 0.70 3.25%
7 to 10 years 5.7 to 7.3 years 0.65 3.75%
10 to 15 years 7.3 to 9.3 years 0.60 4.50%
15 to 20 years 9.3 to 10.6 years 0.60 5.25%
over 20 years 10.6 to 12 years 0.60 6.00%
12 to 20 years 0.60 8.00%
over 20 years 0.60 12.50%

Page 141
interest rate volatilities across different maturities. A separate maturity ladder must be constructed for
each currency in which the bank has a significant trading position. No offsetting is allowed among
maturity ladders of different currencies. This has a considerable impact upon financial institutions
that trade in one currency and hedge in another currency (due to the high correlation between the two
currencies). For instance, an institution that entered into a swap in U.S. dollars and then performed an
exactly offsetting swap in Canadian dollars would be only exposed to some residual foreign exchange
risk and cross-currency basis risk in economic terms. The BIS methodology, however, imposes an
onerous amount of capital for this trade and its hedge.
The first step in the maturity method consists of allocating the marked-to-market value of the
positions to each maturity band. Fixed-rate instruments are allocated according to the residual term to
maturity, and floating-rate instruments according to the residual term that applies to the next
repricing date.
Derivatives, such as forwards, futures, and swaps, are converted into long and short positions in the
underlying positions. Options are treated separately (see below). For example, a long one-year
forward contract on a two-year bond is equivalent to a short position in the six- to 12-month maturity
band for an amount equal to the discounted value of the forward price of the bond, and a long
position in the one- to two-year maturity band for the same market value. In the case of swaps, the
paying side is treated as a short position and the receiving side as a long position on the relevant
underlying instruments. Offsetting is only allowed for matched positions in identical instruments that
have exactly the same issuer.
In the second step the positions in each maturity band are risk-weighted according to the sensitivities
given in Table 4.2.
The third step consists of calculating capital requirements for general market risk according to the
following principles:
1. Vertical disallowance to account for basis risk. In each maturity band, the matched weighted
position is awarded a capital charge of 10 percent. The unmatched positions in each maturity band are
considered in the calculation, related to the horizontal disallowance and a parallel shift in the yield
curve (principles 2 and 3).

Page 142
2. Horizontal disallowance to account for the risks caused by possible twists in the yield curve. The
matched weighted positions in each zone (zones 1, 2, and 3, respectively), between adjacent zones
(between zones 1 and 2, then between zones 2 and 3), and between the two extreme zones (between zones 1
and 3) are allocated a capital charge given in Table 4.3. Again, only the unmatched positions at each step
are considered in the remaining calculations, related to a parallel shift in the yield curve (principle 3).
3. To account for the risk associated with a parallel shift in the yield curve, the residual unmatched
weighted positions are given a capital charge of 100 percent.
The example presented in Table 4.4 illustrates the allocation process to each maturity band, and the
calculation of the capital charge for general market risk.
TABLE 4.3
Horizontal Disallowances for the Risk Related to Twists in the Yield Curve
Between Adjacent
Zones Time Band Within the Zone Zones Between Zones 1 and 3
Zone 1 0–1 month
1–3 months 40%
3–6 months
6–12 months 40%
Zone 2 1–3 years
2–3 years 30% 100%
3–4 years
Zone 3 4–5 years 40%
5–7 years
7–10 years
10–15 years 30%
15–20 years
over 20 years

Page 143
Note that there is vertical disallowance only in zone 3 for the seven- to 10-year maturity band. There
is no horizontal disallowance within zones 2 and 3, since there are no offsetting positions between
time bands within each of these two zones. However, there is horizontal disallowance within zone 1,
and between zones 1 and 3. The short risk-weighted position in the three- to six-month time band
partially offsets the long positions in the adjacent time bands in zone 1. Then, after vertical
disallowance in the seven- to 10-year time band for $0.5 million, the net unmatched position in zone 3
becomes a net short position of $5.125 million.
Given the net long position for $1.125 million in zone 2, there is partial offsetting for this amount
between zones 2 and 3, which leaves a net unmatched position of 0 in zone 2 and a net short position
of $4 million in zone 3. After horizontal disallowance in zone 1, the net unmatched position becomes
a net long position of $1 million in this zone.
Finally, there is partial offsetting for $1 million between zones 1 and 3, which leaves an overall net
unmatched position of $3 million.
The total capital charge is (in $ million):
• For the vertical disallowance (basis risk) $ 0.050
• For the horizontal disallowance in zone 1 (curve risk) $ 0.080
• For the horizontal disallowance between adjacent zones (curve risk) $ 0.450
• For the horizontal disallowance between zone 1 and 3 (steepening of the curve risk) $ 1.000
• For the overall net open position (parallel shift risk) $ 3.000
Total $ 4.580
2.1.3—
Treatment of Options
There are three different approaches. The "simplified approach" applies to banks that buy options but
do not write them, while the "delta-plus method" and the "scenario approach" should be used by
banks that both buy and write options.
(i)—
Simplified Approach
Table 4.5 shows the capital charge according to the simplified approach. As an example, suppose the
bank is long 100 shares

Page 144
TABLE 4.4
Illustration of the Calculation of the Capital Charge to Cover General Market Risk for Interest Rate Instruments (Except Options)
Portfolio:
A. Qualifying bond with a $13.33 million market value, a residual maturity of eight years, and a coupon of 8%.
B. Government bond with a market value of $75 million, a residual maturity of two months, and a coupon of 7%.
C. Interest rate swap at par value, i.e., with a zero net market value, with a notional amount of $150 million, where the bank receives floating and pays fixed, with the next fixing in nine months,
and a residual life of eight years.
D. Long position in interest rate futures contract with six-month delivery date, for which the underlying instrument is a government bond with a three-and-a-half-year maturity and a market value
of $50 million.
Zone 1 (months) Zone 2 (years) Zone 3 (years)
Time band
Coupon >3% 0–1 1–3 3–6 6–12 1–2 2–3 3–4 4–5 5–7 7–10 10–15 15–20 >20
Coupon <3% 0–1 1–3 3–6 6–12 1–1.9 1.9–2.8 2.8–3.6 3.6–4.3 4.3–5.7 5.7–7.3 7.3–9.3 9.3–10.6 10.6–12 12–20 >20
(table continued on next page)

Page 145
(table continued from previous page)
Zone 1 (months) Zone 2 (years) Zone 3 (years)
Positions
A +13.33
B +75 Qual.
Gov.
C +150 -150
D -50 Swap +50 Swap
Fut. Fut.
Weight (%) 0.00 0.20 0.40 0.70 1.25 1.75 2.25 2.75 3.25 3.75 4.50 5.25 6.00 8.00 12.5
Postion x +0.15 -0.20 +1.05 +1.125 +0.5
Weight -5.625
0.5 × 10%
Vertical = 0.05
Disallowance
Horizontal 0.20 × 40% = 0.08
Disallowance 1
Horizontal 1.25 × 40% = 0.45
Disallowance 2
Horizontal
Disallowance 3 1.0 × 100% = 1.0

Page 146
Table 4.5
Capital Charge for Options According to the Simplified Approach
Position Treatment
Long cash and long put The capital charge is the market value of the underlying security multiplied by the sum
Or of specific and general market risk charges for underlying, less the amount the option
Short cash and long call is in the money (if any), bounded at zero.
The capital charge will be the lesser of:
Long call • The market value of the underlying security multiplied by the sum of specific and
Or general market risk charges for the underlying.
Long put • The market value of the option.
currently valued at $10, and has a put option on these shares with a strike price of $11. The capital charge would be:
(ii)—
Delta-Plus Approach
For the purpose of calculating the capital charges related to general market risk, the option is first considered as its
"delta equivalent" in the underlying instrument. The delta equivalent is then allocated into the time band corresponding
to the maturity of the option (see example in Table 4.4). 2
Then, two additional capital charges are added. The first one adjusts the capital charge for gamma risk or convexity
risk,3 i.e.,
This is simply the second-order term in the Taylor expansion4 of the option price formula, where ∆V denotes the
change in the

Page 147
value of the underlying. For interest rate products, the calculation of the charge is based upon the
assumed changes in yield in the maturity band, as given in Table 4.2. For equities and foreign
exchange and gold the price change in the calculation is taken as a fixed change of 8 percent, while for
commodities it is taken as 15 percent (the approach is illustrated in Table 4.6).
The second capital charge compensates for vega risk, i.e.,
where vega is the sensitivity of the option price to a change of one unit of volatility, σ.
This vega charge represents the impact that a 25 percent increase or decrease in volatility would have
on the value of the position.
(iii)—
Scenario Matrix Approach
The scenario matrix approach adopts as a capital charge the worst loss that might arise from the
positions in a series of scenarios. The scenarios are generated by a grid that allows for a combination
of possible values of the underlying price, the volatility, and the cost of carry. The range of values that
is considered in the calculation is the same as for the delta-plus approach.
Table 4.6
Delta-plus Approach for an Equity Option
Consider a short position in a European one-year call option on a stock with a striking price of $490. The underlying
spot price is $500, the risk-free rate is 8% per annum, and the annualized volatility is 20%. The option value is
$65.48, with a negative delta and gamma of –0.721 and –0.0034, respectively, corresponding to a $1 change in the
underlying price; its vega is 1.68 associated with a change in volatility of one percentage point.
The three components of the capital charge are:
Delta equivalent: $500 * 0.721 * 8% = $28.84
Gamma adjustment: 1/2 * 0.0034 * ($500 * 8%)2 = $ 2.72
Vega adjustment: 1.68 * (25% * 20) = $ 8.40
Total $39.96

Page 148
2.2—
Equity Risk
The charge for the general market risk incurred by equity positions is 8 percent of each net position.
The capital charge for any specific risk is 8 percent, unless the portfolio is both liquid and well
diversified, in which case the charge is 4 percent.
Equity derivatives are treated in the same way as interest rate derivatives. While there is no specific
charge when the underlying is a government security or a market rate such as LIBOR, for diversified
broad market indices there is a specific risk charge of 2 percent of the underlying market value.
The example given in Table 4.6 illustrates the delta-plus approach as it applies to equity option
positions. Note that the gamma adjustment is based on an 8 percent move in the stock price. If the
underlying were a commodity, the adjustment would be based on a 15 percent move in the
underlying price, and the delta-equivalent would have been allocated to the time band corresponding
to the maturity of the option (see Table 4.8).
2.3—
Foreign Exchange Risk, Including Gold Price Risk
There are two steps in the calculation of the capital charge. First, the exposure in each currency is
measured and, second, the net long and net short exposures in all currencies are translated into an
overall capital charge according to a rule called the "shorthand method."
The measurement of the exposures is straightforward. It consists of the net spot position, the net
forward position, 5 the delta-equivalent for options as discussed in Section 2.1.3, accrued interest and
expenses, and other future income and expenses which are already fully hedged.
The capital charge is the absolute value of 8 percent of the greater of the net open long positions and
the net open short positions in all currencies, plus 8 percent of the absolute value of the net open
position in gold plus the gamma and vega adjustments for options. The example in Table 4.7
illustrates the application of the rule.

Page 149
Table 4.7
Shorthand Approach to Capital Charge for Foreign Exchange and Gold Risk
2.4—
Commodities Risk
Commodities are broadly defined as physical products that can be traded on an organized market, such as
agricultural products, oil, gas, electricity, and precious metals (except gold, which is treated as a foreign
currency). The risk of commodities is often more complex to measure than that of other financial
instruments as the markets are less liquid, prices are affected by seasonal patterns in supply and demand,
and inventories play a critical role in the determination of the equilibrium price.
The main components of market risk are:
• Outright price risk, i.e., the risk of price movements in the spot prices.
• Basis risk, i.e., the risk of a movement in the price differential between different but related commodity
prices. This risk is inherent for energy products whose prices are quoted as a spread over a benchmark
index.
• Interest rate risk, i.e., the risk of a change in the cost of financing any investment in the commodity (a key
component in the ''cost of carry").
• Time spread risk, or forward gap risk, i.e., the risk of movements in forward commodity prices for
reasons other than a change in interest rates; the shape of the forward

Page 150
curve is a function of supply and demand in the short run, and fundamental factors in the longer run.
• Options risk, i.e., delta, gamma, and vega risk as already discussed for other classes of products.
The standardized model for commodities is somewhat similar to the maturity ladder approach for
interest rate products. In effect, it attempts by means of a simple framework to capture directional
risk, curve risk, and time spread risk.
First, positions are converted at current spot rates into the reporting currency, and placed in the
relevant time band. Forwards, futures, and swaps are decomposed into a combination of long and
short positions (as for interest rate products). The delta equivalent of options is placed in the time
band corresponding to the maturity of the option.
To capture spread risk and some of the forward gap risk, the matched position in a time band is
allocated a capital charge of 3 percent. The unmatched position is carried forward into the nearest
available time band at a cost of 0.6 percent per maturity band. For example, if it is moved forward by
two maturity bands, it is charged 2 * 0.6% = 1.2%. At the end of the process, the net unmatched
position is given a capital charge of 15 percent.
The example in Table 4.8 illustrates the principle of the maturity ladder for commodities.
3—
The Internal Models Approach
Nowadays, those institutions that trade in financial products rely on their proprietary expertise in
modeling as much as they rely on traditional trading skills. The risk that these models will be wrong
or wrongly implemented—what is known in the derivatives industry as "model risk"—is likely to
remain an issue since it is inherent in the trading of derivatives. Indeed, the ability of a trading
institution to remain profitable relies in part on the skill of its financial engineers and traders to build
and continually renew the appropriate pricing and hedging models. State-of-the-art modeling
provides many institutions with a unique competitive edge.
Pricing models are kept relatively secret, although most of them are based on published papers in
academic journals. However,

Page 151
Table 4.8
Maturity Ladder Approach for Commodities
Spread Capital
Time Band Charge Position Capital Charge
0–1 m 1.5% —
1–3 m 1.5% —
3–6 m 1.5% Long $600 Matched position:
Short $1,000 $600 × 3% = $18
$400 carried forward 2 time bands:
$400 × 2 × 0.6 = $4.8
6–12 m 1.5% —
1–2 y 1.5% Long $500 Matched position:
$400 × 3% = $12
$100 carried forward 1 time band:
$100 × 0.6 = $0.6
2–3 y 1.5% Short $300 Matched position:
$100 × 3% = $3
Over 3 y 1.5% —
Net unmatched position:
$200 × 15% = $30
Total $68.4
the implementation and calibration of these models requires ingenuity, strong numerical and computer
skills, and a good understanding of the products and the markets. Very few professionals are able to
produce this elaborate cocktail.
The proprietary models that are used in pricing market positions are also used for position risk
management. This is how banks derive risk exposures such as deltas, gammas, vegas, and other "greeks"
(see Chapter 5). However, as regularly reported in the financial press, using the wrong model not only leads
to large trading losses, but can also lead to a poor assessment of market risk exposure.
The regulators accept that it is in the nature of the modern banking world that institutions will use different
assumptions and modeling techniques. The regulators take account of this for their

Page 152
own purposes by requiring institutions to scale up the value-at-risk number derived from their
internal model by a factor of 3, referred to in the following as the "multiplier." This multiplier can be
viewed as insurance against model risk, imperfect assessment of specific risks, and other operational
risks. Alternatively, it might be regarded as a safety factor that guards against "nonnormal" market
moves. However, as we discuss later on, the use of multipliers in this way is open to criticism.
3.1—
Quantitative and Modeling Requirements
The "internal model" approach is intended to capture all the material market risks of the bank's
trading positions. The technique most widely recognized by the financial industry and regulators for
the assessment of market risk in a portfolio context is the value-at-risk methodology described in
Chapter 5.
Although each institution has some discretion in the choice of the risk factors used in the VaR model,
these risk factors should be selected with great care so as to guarantee the robustness of the model.
Oversimplification and a failure to select the risk factors that are inherent in the trading positions may
have serious consequences, as the VaR model would be likely to miss the financial exposures
generated by risks such as basis risk, curve risk, or spread risk.
These shortcomings are likely to be revealed when back-testing the model, and may lead to penalties
in the form of the imposition by the regulators of a multiplier greater than the usual multiplier of 3.
Market risk can be broken down into four categories: interest rate risk, equity risk, exchange rate risk,
and commodity price risk:
• Interest rate risk modeling applies only to the trading book. The base yield curve in each currency
(government curve or swap curve) should be modeled with a minimum of six risk points, i.e., six
yields with different maturities such as one month, six months, one year, etc. The other relevant yield
curves, e.g., the yield curves of corporate debt and provincial yield curves for Canada, 6 are defined
with regard to the base curve by the addition of a spread

Page 153
(positive or negative). The model should also incorporate separate risk factors to capture spread risk.
• Equity price risk modeling should incorporate risk factors corresponding to each of the equity
markets in which the trading book holds significant positions. At a minimum, there should be a risk
factor designed to capture market-wide movements in equity prices, e.g., the broad market index in
each national equity market. This could be used to assess both market risk and idiosyncratic risk,
according to the capital asset pricing model (CAPM). The most extensive approach would be to
assign risk factors that correspond to each asset in the portfolio.
• Exchange rate risk modeling should include risk factors corresponding to the individual currencies
in which the trading and banking books have positions.
• Commodity price risk should incorporate risk factors that correspond to each of the commodity
markets in which the trading and banking books have significant positions. The model should
account for variations in the convenience yield. 7 It should also encompass directional risk to capture
exposure from changes in spot prices, forward gap and interest rate risk to capture exposure to
changes in forward prices arising from maturity mismatches, and basis risk to capture the exposure to
changes in price relationship between similar commodities (e.g., energy products that are defined
relative to a price for a benchmark crude oil such as WTI).
As we explain in Chapter 5, the confidence level and holding period of any VaR calculation are
critical to the validity of the risk assessment. The 1996 Amendment requires VaR to be derived at the
99 percent (one-tailed)8 confidence level, using a 10-day holding period. In effect, this means the
regulators are asking banks to take into account in their VaR figure the risk that they might not be
able to liquidate their positions for a period of 10 days. However, in the initial phase of
implementation of the internal model, the BIS allows the 10-day VaR to be proxied by multiplying
the one-day VaR by the square root of 10, i.e., 3.16.9

Page 154
Table 4.9
Multiplier Based on the Number of Exceptions in Back-Testing
Number of Exceptions Multiplier
4 or fewer 3.00
5 3.40
6 3.50
7 3.65
8 3.75
9 3.85
10 or more 4.00
The daily regulatory capital requirement corresponds to the maximum of previous day's VaR (VaRt-1)
and the average of daily VaR experienced over the preceding 60 business days
scaled up by the multiplier k, which normally should be equal to 3:
As we discussed in Section 2.1, this arbitrary multiplier is intended to compensate for model errors,
and the imperfect assessment of specific risks and operational risks. The regulators can increase it, up
to 4, if the models do not meet back-testing requirements (Table 4.9).
Institutions are allowed to take into account correlations among risk categories. Volatilities and
correlations should be estimated using historical data, with a minimum history of 250 days, 10 i.e.,
approximately one year of business days. Market parameters should be updated at least once every
three months, or more frequently if market conditions warrant. If empirical correlations between risk
categories are unavailable, then the aggregate VaR is calculated as the simple arithmetic sum of the
VaR for each block, i.e., equity, interest rate, foreign exchange, and commodities. In that case, the
aggregate VaR does not benefit from the risk reduction that results from any diversification across
risk classes.
The internal model should capture not only linear risks, known as delta risks, but also nonlinear risks,
such as the convex-

Page 155
ity risk (gamma) and volatility risk (vega) inherent in options positions. One important point is that
the choice of the VaR methodology is otherwise left to the institution. As Chapter 5 describes, it can
choose to implement historical simulation, full Monte Carlo simulation, or other pseudo-analytic
methods based on the Greeks (variance-covariance approach).
Banks that cannot meet all the requirements for internal models are allowed to use a combination of
standard models and internal models, but are expected to move towards the full internal models
framework. Each risk category, however, must be measured by means of a single approach. If a
combination of approaches is used, then the total capital charge is determined by a simple arithmetic
sum. This, of course, cannot take into account the possible correlation effects between the risk
categories.
3.2—
Specific Risk
As we explained at the beginning of this chapter, according to the 1996 Amendment banks are
required to hold capital in support of the "specific risk" associated with any debt and equity positions
in their trading books. In return, no further capital charges are allocated to these positions in respect of
credit risk. In other words, specific risk is simply a substitute for credit risk for traded on-balance-
sheet products.
Derivative instruments incur a specific risk capital charge when the underlying is subject to specific
risk. Thus, when they are traded on an exchange, there is no specific risk charge for interest rate and
currency swaps, FRAs, forward foreign exchange contracts, interest rate futures, and futures on an
interest rate index. However, when the instruments are traded over-the-counter (OTC), and thus do
not benefit from the credit guarantees extended by an exchange environment, the instruments
generate counterparty risk and are charged a capital amount to cover their credit risk exposure
(according to rules of the 1988 Accord).
The capital charge for specific risk can be determined either by using internal models, scaled up by a
multiplier of 4, or the standardized approach.
So how should such a charge be determined using internal models? 11

Page 156
The new 1998 regulatory framework views specific risk, and consequently credit risk, as an
outgrowth of market risk. As such it should be modeled using assumptions that are consistent with
the market risk model. This is a significant improvement with respect to the 1988 Accord, where the
credit risk capital charge was calculated according to somewhat arbitrary ratios that did not correctly
account for the specificity of the instruments. 12
At CIBC, the internal model for bonds captures both spread risk and credit risk. Credit risk arises out
of default events, but also from credit migration, i.e, when a company's credit rating is upgraded or
downgraded. An approach such as CreditMetrics, proposed by JP Morgan (1997), provides a good
practical framework for building an internal model that relates to the specific risk of bonds (see
Chapter 8).
For equities, the approach is different since market risk, measured by the volatility of stock returns,
already captures both general market risk and specific risk. In other words, both the market risk and
the default risk of stocks are already fully accounted for by the current spot price. So how can we
break the total risk for a stock into its general market risk and specific risk components? To do this,
we turn to the statistical properties of a "single-index model," known also as the market model.13 The
fundamental idea is that the rate of return on any stock i is related to some common index I by a
linear equation of the form:
where
Ri is the rate of return on stock i
αi is the constant component of the return of stock i
I is the value of the index
βi is a measure of the average change in Ri as a result of a given change in the index I
ui is a deviation of the actual observed return from the regression line αi + βi Rm, i.e., the error term,
which is assumed to be normally distributed, N(0,σui)
The index generally used for this model is the rate of return on the market portfolio (approximated in
the United States by the S&P500 Index or by the NYSE Index), which we denote Rm. The

Page 157
crucial assumption is that for every pair of stocks (i,j) the error terms are uncorrelated; i.e., Cov (ui, uj)
= 0. The error term is also assumed to be uncorrelated with the market portfolio; i.e., Cov (ui,Rm) = 0.
The parameters of Equation (2) are estimated in practice by using the ex-post historical rates of
return, and by running a time series regression. It follows that:
Taking the variance of both sides of Equation (2) we obtain:
The total risk of a security, as measured by its variance, can be divided into two components:
(i) – systematic risk, or general market risk, which is nondiversifiable and associated with
market fluctuations, where σm denotes the variance of the market return
(ii) – idiosyncratic risk, or specific risk, which can be eliminated through diversification
Given a stock, or a portfolio, whose price is denoted Si, the general market risk (GMR) of the position
is, according to the market model:
and its specific risk (SR) is:
These risks can be easily aggregated. For a portfolio with a total value of P composed of n securities
Si, i = 1, . . . , n, the general market risk for the portfolio is:

Page 158
where represents the beta of the portfolio P, which is the weighted average of
the betas of the individual stocks, with the individual weight, xi = Si/P, being the proportion of stock i
in the portfolio.
Under the assumption that the error terms are uncorrelated, the specific risk for the portfolio is
simply:
3.3—
New Capital Requirements
Banks are allowed, under the 1996 Amendment, to employ a new category of capital known as tier 3
capital. This consists mainly of short-term subordinated debt, subject to certain conditions. However,
banks can use tier 3 capital only to meet their daily market risk capital requirement as defined in
Equation (1). Banks should first allocate tier 1 and tier 2 capital to meet credit risk capital
requirements according to the 1988 Accord, so that together they represent 8 percent of the risk-
weighted assets. The risk-weighted assets should be adjusted for the positions that are no longer
subject to the 1988 credit risk rules, i.e., the traded instruments on the balance sheet such as bonds,
and equities that are already subject to the capital charges for specific risk.
Then, the bank should satisfy a second ratio that compares the eligible capital to the risk-weighted
asset equivalent. The risk-weighted asset equivalent is simply the sum of the risk-weighted on-
balance-sheet assets, the risk-weighted off-balance-sheet items, and 12.5 times the market risk capital
charge, where 12.5 is the reciprocal of the minimum capital ratio of 8 percent.
Eligible capital is the sum of, first, the whole bank's tier 1 capital; second, all of its tier 2 capital under
the limit imposed by the 1988 Accord (i.e., tier 2 capital may not exceed 50 percent of tier 1 capital);
and, third, some of its tier 3 capital. Banks will be entitled to use tier 3 capital solely to satisfy the
market risk capital charge, under some limiting conditions. The market risk capital charge should be
met with tier 3 capital, and by means of the additional tier 1 and tier 2 capital not allocated to credit
risk. Tier 1 capital

Page 159
should constitute the most substantial portion of the bank's capital, with the final rule stating that:
• At least 50 percent of a bank's qualifying capital must be tier 1 capital, with term subordinated debt
not exceeding 50 percent of tier 1 capital.
• The sum of tier 2 and tier 3 capital allocated for market risk must not exceed 250 percent of tier 1
capital allocated for market risk; i.e., 28.57 percent of market risk capital charge should be met with
tier 1 capital. 14
Suppose that a bank has:
• Risk-weighted assets that amount to 7500
• A market risk capital charge of 350
The bank capital is assumed to be constituted of tier 1 capital for 700, tier 2 capital for 100, and tier 3
capital for 600. Does this bank meet the BIS capital ratio requirements? The example in Table 4.10
illustrates the calculation of the capital ratio and one possible allocation of capital.
From the table we can see that, after allocating tier 1 and tier 2 capital to credit risk, there is 200 of
unused tier 1 capital left available to support market risk. This means that the maximum eligible tier 3
capital is only 500, according to the 250 percent rule. After the full allocation for credit risk, 250 of
tier 3 capital is left unused, but eligible; there is also 100 unused tier 3 capital that is not eligible.
In this example, the capital ratio is greater than the minimum of 8 percent, since the numerator of the
capital ratio is the sum of the minimum capital requirement (8 percent) and the unused portion of tier
1 capital.
3.4—
Back-Testing
Back-testing a bank's internal models provides a key test of how accurate and robust the models are.
In effect, back-testing compares the bank's internally generated VaR figures with the actual
performance of the bank's portfolio over an extended period of time. It is a vital part of the regulatory
oversight of the use of internal models.

Page 160
Table 4.10
Calculation of the Capital Ratio Under the 1996 Amendment
Minimum Eligible Capital
Risk-Weighted Capital Minimum Capital for (Excluding Unused Tier Unused but Eligible Unused but Not Eligible
Assets Charge (8%) Available Capital Meeting Requirement 3) Tier 3 Tier 3
Credit risk 7,500 600 Tier 1 700 Tier 1 500 Tier 1 700
Tier 2 100 Tier 2 100 Tier 2 100
Market risk 4,375 350 Tier 3 600 Tier 1 100 Tier 3 250 Tier 3 250 Tier 3 100
(i.e., 350 × 12.5) Tier 3 250
Total 1050 250
Capital ratio: Excess tier 3
1,050/11,875 = capital ratio:
8.8% 250/11,875 =
2.1%

Page 161
When they are being employed in relation to regulatory capital requirements, back-tests must
compare daily VaR measures calibrated to a one-day movement in rates and prices and a 99 percent
(one-tailed) confidence level, against two measures of the profit & loss (P&L):
• The actual net trading P&L for the next day
• The theoretical P&L, also called ''static P&L," that would have occurred if the position at the close
of the previous day had been carried forward to the next day 15
Assuming that the risk factors are correctly modeled and that markets behave accordingly, then we
would expect the absolute value of actual P&L over the last 250 days to be greater than the calculated
VaR figure on only two and a half days on average (i.e., in practice, three days).16
Regulators stipulate that back-testing should be performed daily.17 In addition, an institution must
identify the number of times that its net trading losses, if any, for a particular day exceeded the
corresponding daily VaR. If the number of exceptions during the previous 250 days is greater than 5,
the multiplier we described earlier in this chapter may be increased, and can rise up to 4 if the
number of exceptions reaches 10 or more during the period (Table 4.9).
However, there is some doubt as to how seriously this rule will be enforced. Exceptions to the rule
are already envisaged by the regulators when abnormal situations occur, such as a market crash, a
major political event, or a natural disaster. In addition, the regulators seem likely to acknowledge the
fact that all financial institutions, including the regulatory bodies, are "learning by doing." It may thus
not be appropriate to penalize an institution by applying a higher multiplier, providing that the
institution reacts quickly to improve its VaR model.
The ISDA/LIBA Joint Models Task Force (ISDA 1996) criticized the scaling factor of 3, suggesting
that the rule should simply be repealed. It considered that a multiplier of any size is an unfair penalty
on banks that are already sophisticated in the design of their risk management system, and in the
modeling of general as well as specific risks. Back-testing is a powerful process with

Page 162
which to validate the predictive power of a VaR model. It is, in effect, a self-assessment mechanism
that offers a framework for continuously improving and refining risk modeling techniques.
The Task Force argued that regulators should use this framework to develop the incentives for banks
to implement best practices: only banks that failed to take appropriate action should suffer a scaling
factor greater than 1. An arbitrarily high scaling factor may even provide perverse incentives to
abandon initiatives to implement prudent modifications of the internal model.
3.5—
Stress Testing
When developing a VaR model, many assumptions have to be made for practical reasons. In
particular, most market parameters are set to match "normal" market conditions. This leaves risk
managers and regulators with a number of practical considerations. How robust is the VaR model?
How sensitive are the VaR numbers to key assumptions?
Value-at-risk models, which calculate the maximum that an institution could lose in a normal day's
trading, work well in normal market conditions, but not in extremes. This is the reason why
regulators require that a bank complement its VaR analysis with a series of stress testings of their
portfolios. Stress scenarios calculate the losses that might arise as the result of imagined crises—
crises relevant to the bank given the nature of its portfolios. (See Chapters 5 and 11 for a detailed
discussion of stress testing for market risk and credit risk models, respectively.)
Regulators require that banks set limits not only for their VaR exposures, but also for their stress
losses.
4—
Pros and Cons of the Standardized and Internal Models Approaches:
A New Proposal—
The "Precommitment Approach"
The standardized approach has been much criticized. It applies the same capital charge to vastly
different financial instruments, e.g., to plain vanilla swaps and highly levered transactions, and it fails

Page 163
to account for any portfolio effects on the true levels of risk (for both credit and market risk).
The internal models approach remedies many of these criticisms, and can be seen as an attempt to
improve the accuracy of the standardized approach. However, some regulators question the ability of
banks to capture properly the key risks embedded in their portfolios, i.e., directional, spread, curve,
volatility, and liquidity risks. 18 They argue that even if banks are now able to develop analytical
approaches to cope with these problems, they do not have the resources to implement the right
infrastructure—especially in terms of their transactions databases and their financial rates databases.
However, the conservative multipliers used in the present approaches are not a panacea. They may
discourage the most sophisticated banks from improving their internal models, at least for regulatory
capital purposes. Worse, they may also induce a distorted allocation of capital.
Rating institutions such as Standard & Poor's have expressed their concern that the new 1998
regulatory framework may substantially reduce the amount of regulatory capital. For on-balance-
sheet traded products such as bonds and stocks, the expensive credit risk capital charge according to
the initial 1988 Accord will be replaced by the less onerous capital charge associated with specific
risk. The net effect, as we discussed earlier, should be an average net capital savings of 20 to 50
percent for the largest trading banks.
Standard & Poor's (1996) argues that market risks in a trading operation are largely overshadowed by
other risks which are difficult to quantify such as operating risks related to employee fraud and
systems failure, legal risk related to the potential for lawsuits from frustrated clients, reputation risk,
liquidity risk, and operating leverage.
In recognition of the weaknesses inherent in both the standardized approach and the internal models
approach, two senior economists at the Board of Governors of the Federal Reserve Board, P. Kupiec
and J. O'Brien (1995b, 1995c, 1995d, 1996) have proposed an alternative approach, the so-called
"precommitment approach" (PCA). The PCA would require a bank to precommit to a maximum loss
exposure for its trading account positions over a fixed period.

Page 164
This maximum loss precommitment would, in effect, form the bank's market risk capital charge.
Should the bank incur trading losses that exceed its capital commitment, it would be subject to
penalties. Violation of the limit would also bring public scrutiny to the bank—a further feedback
mechanism for sound management.
Under the PCA, the bank's maximum loss precommitment would reflect the bank's internal
assessment of risks, including formal model estimates as well as management's subjective judgments.
The PCA approach is an interesting initiative since it aims at replacing regulatory capital
requirements that are based on ex ante estimates of the bank's risks, with a capital charge that is set
endogenously, through the optimal resolution of an incentive contract between the bank and its
regulators.
Indeed, it can be shown that the PCA takes the form of a put option written on the bank's assets and
issued to the regulators. The value of this liability for the bank increases with the penalty rate, set by
the regulator, and the riskiness of the bank's assets, while it decreases with the strike price of the put,
i.e., the precommitment level. When the bank increases the risk of its assets, it increases the value of
its precommitment liability, which is more or less than offset by the increase in the value of the
fixed-rate deposit insurance (see Chapter 2).
Each bank would have to discover the optimal trade-off between the riskiness of its trading book and
the level of precommitted capital. Its objective in doing so would be to maximize the shareholder
value and to minimize the exposure of the deposit insurance institution. 19
The PCA has been criticized by Gumerlock (1996). Gumerlock compares the PCA to speed limits
and fines for reckless driving, while he compares the internal models approach to inspections that
guarantee that vehicles are roadworthy at all speeds and on all types of roads and weather conditions.
One key point to remember here is that risk management consists of much more than internal models.
They are only one important element in risk measurement. In practice, risk managers should rely on
their experience, judgment, and controls, and not simply on formulas that translate model results into
capital charges. The PCA is interesting in that it attempts to take the multiple facets of risk
management into account.

Page 165
5—
Comparisons of the Capital Charges for Various Portfolios According to the Standardized and
the Internal Models Approaches
In general, the standardized approach produces a much larger capital charge than any reasonable
VaR-based model. At CIBC we have compared the capital charges attributed to general market risk
using actual market positions over a six-month period. The capital savings, i.e., the reductions in the
capital charge realized by adopting our internal model instead of the standardized approach, vary
between a low of 60 percent to a high of 85 percent. The capital saving is higher when the portfolio is
highly diversified across maturities and across countries, and when the portfolio is relatively well
hedged in a VaR sense, i.e., its VaR exposure is small. The multiplier of 3 makes the capital charge
generated by the internal model quite sensitive to market risk exposure.
To gain a better understanding of the extent of the differences in capital charges generated by the
standardized method and CIBC's internal method, we investigated four basic portfolios and a
relatively well-diversified cross-currency portfolio. The portfolio contents are given in Table 4.11.
The cross-currency portfolio has products in both Canadian and U.S. dollars covering a wide range of
maturities. These portfolios are limited to linear interest rate products. All bonds are considered to be
government issue to avoid the calculation of a specific risk capital charge. All of the following
examples focus only on general market risk.
To illustrate the differences between the two methods in capturing the portfolio effects, we consider
portfolios with short and long positions, first in a single currency, and then in two different
currencies, namely the U.S. and the Canadian dollar. The interest rate curves that we used to perform
the computations are given in Table 4.12 and correspond to market data as of April 5, 1997.
The first portfolio is simply a plain vanilla swap with a corporation, with the bank receiving the fixed
rate. The internal model is a simple VaR model where the risk factors are the zero-coupon rates for
the maturities shown in Table 4.12. The changes in those rates are supposed to follow a multivariate-
normal distribution; Table 4.13 provides the volatilities for the U.S. swap curve. 20

Page 166
Table 4.11
Portfolios of Fixed-Income Instruments
Portfolios
1 USD 100 million 10-year swap, receive fixed against three-month LIBOR; counterparty is a corporation
Portfolio 1
2 + 100 million USD 5-year swap, pay fixed against three-month LIBOR; counterparty is a corporation
• long a 100 million USD 10-year government bond with a 6.50% semi-annual coupon
3 • 100 million USD 10-year swap, pay fixed against 3-month LIBOR; counterparty is a corporation
• 100 million USD 10-year swap, pay fixed against 3-month LIBOR; counterparty is a corporation
4 • 140 million CAD 10-year swap, receive fixed against 3-month LIBOR; counterparty is a corporation
5 CAD
• long 100 million 3-month T-bill
• long 75 million 8% government bond maturing in 20 years
• long 25 million 8% government bond maturing in 3 years
• short 25 million 8% government bond maturing in 12 years
• 100 million 5-year swap, receive fixed against 3-month LIBOR
• 100 million 20-year swap, pay fixed against 3-month LIBOR
USD
• short 300 million 3-month T-bill
• long 100 million 6-month T-bill
• short 200 million 9-month T-bill
• long 100 million 6.5% government bond maturing in 4 years
• long 200 million 6.7% government bond maturing in 5 years
• long 100 million 7% government bond maturing in 12 years
• 100 million 2-year swap, pay fixed against 3-month LIBOR
• 100 million 10-year swap, pay fixed against 3-month LIBOR
• 100 million 20-year swap, pay fixed against 3-month LIBOR
The VaR for this swap is $US927,000, while the sum of the VaR for each risk point on the curve is
$US962,549. 21 As the changes in the rates are highly correlated, the risk reduction due to the
portfolio effect is relatively modest, i.e., 3.7 percent in this example. The application of the
standardized approach for general market risk,

Page 167
Table 4.12
Interest Rate Curves Zero-Coupon Curves with Continuously Compounded Rates (April 5, 1997)
U.S. (USD) Canada (CAD)
Term Treasuries Swaps Treasuries Swaps
On 5.31% 3.04% 3.00% 3.00%
1m 5.32% 5.50% 2.92% 3.10%
2m 5.31% 5.55% 3.05% 3.18%
3m 5.39% 5.56% 3.15% 3.25%
6m 5.44% 5.62% 3.46% 4.70%
9m 5.45% 5.70% 3.75% 5.09%
1y 5.46% 5.79% 3.89% 5.34%
1.25y 5.73% 5.88% 4.28% 5.50%
1.5y 5.94% 5.96% 4.57% 5.64%
1.75y 6.12% 6.03% 4.92% 5.75%
2y 6.24% 6.10% 5.17% 5.85%
3y 6.41% 6.41% 5.72% 6.59%
4y 6.47% 6.56% 6.06% 6.62%
5y 6.54% 6.66% 6.27% 6.58%
7y 6.56% 6.66% 6.55% 7.13%
10y 6.61% 6.66% 6.96% 7.73%
as presented in Section 2.1.2, is shown in Table 4.14. It produces a capital charge of $US3,750,000.
The capital charges calculated according to the standardized and the internal model approaches are shown in Table 4.15. For this 10-year
swap, the adoption of the internal model does not realize any capital saving, but on the contrary generates a capital surcharge of 132
percent.
There is also a capital surcharge of 103 percent for the second portfolio, which consists of long and short positions in two plain vanilla
swaps of different maturities, but in the same currency, the U.S. dollar. The bank receives a fixed rate on the 10-year swap, and pays fixed
on the five-year swap. Since there is partial offsetting of cash flows up to five years, the portfolio effect is expected to be more substantial
than for the first portfolio.
Table 4.13 shows the details of the derivation of the VaR number. The standardized approach for general market risk is detailed

Page 168
Table 4.13
Internal Model for Portfolios 1 and 2
DV01 (USD) Volatility (bp) VaR/Risk Point (USD)
Term Portfolio 1 Portfolio 2 σ Portfolio 1 Portfolio 2
3m (2,459) 3.59 20,588
6m 28 3.35 215
9m 123 3.46 988
1y 162 3.58 1,350
1.25y 195 3.95 1,794
1.5y 230 4.33 2,319
1.75y 264 4.70 2,894
2y 746 2 5.08 8,824 27
3y 1,681 5 5.29 20,742 63
4y 2,092 6 5.50 26,808 81
5y 3,579 (34,320) 5.50 45,897 440,110
7y 7,308 7,308 5.63 95,878 95,878
10y 58,138 58,128 5.42 734,252 734,252
Notes:
DV01, denotes the sensitivity of the position to a fall of 1 bp in the corresponding zero-coupon rate, and is expressed in
currency units.
σ denotes the daily volatility of the zero-coupon rate and is expressed in bp.
VaR/risk point denotes the VaR for the corresponding zero-coupon rate, at the 99% confidence level (one-tailed) and
for a one-day horizon, i.e., 2.33 σ |DV01|, assuming that interest rate changes are normally distributed.
Portfolio 1 Portfolio 2
(1)Sum of the VaR/risk point = 962,549 USD = 1,270,411 USD
(2) VaR = 927,000 USD = 407,532 USD
Portfolio effect: (1) – (2) = 35,549 USD = 862,879 USD
in Table 4.14, and shows a capital charge of $US1,845,000, with $US1 million related to the risk of a
parallel shift in the yield curve, and $US845,000 to compensate for curve risk. In this case the cash
flows are not well distributed among the various buckets. As a consequence, there is only a small
capital charge for basis risk and curve risk among the different zones of the interest rate curve.
The third portfolio consists of a long government bond position that is hedged by means of a swap of
the same tenor (10 years,

Page 169
in our example), and in the same currency. The capital saving is 62 percent as shown in Table 4.16. In
this case, the position is relatively well hedged in a VaR sense, since its VaR exposure is only
$US19,068. The internal model, with its multiplier of 3, greatly benefits from this situation with
respect to the standardized approach.
The fourth portfolio is constituted of two 10-year swaps, a long and a short position, this time in two
different currencies, the U.S. dollar and the Canadian dollar. In this instance the capital saving is 11.5
percent. The calculations are detailed in Tables 4.16 and 4.17. For this portfolio the internal model
benefits from the diversification of the portfolio across two different currencies. The standardized
approach treats each currency independently, adding the capital charges without any of the benefits
from diversification and hedging across two currencies.
Finally, the fifth portfolio reveals the full benefit of the internal model when the bank's position is
well diversified across maturities and countries. Here, we obtain capital savings of 51 percent (Table
4.18).
6—
Conclusions
The BIS 1998 framework for capital requirement represented a big leap forward in the risk
management of financial institutions. The fact that banks were required to hold capital to cover
market risk associated with their trading book, and foreign exchange and commodity positions in both
the trading and the banking books, helped to change their business model. All of a sudden, there were
considerable incentives for banks to develop their own internal VaR model for both regulatory capital
purposes, but also to closely monitor their risks, and actively manage the risk/return trade-off and the
pricing of new deals.
Since January 1998, leading banks have put in place internal models for the measurement of market
risk. The next challenge is for those banks to develop appropriate internal models for credit risk, and
then to implement an integrated framework for market risk and credit risk to fully account for
portfolio effects within, and across, all types of risk.

Page 170
Table 4.14
Standardized Approach for General Market Risk: Portfolios 1 and 2
Portfolio 1 Zone 1 (months) Zone 2 (years) Zone 3 (years)
Time band
Coupon >3% 0–1 1–3 3–6 6–12 1–2 2–3 3–4 4–5 5–7 7–10 10–15 15–20 >20
Coupon <3% 0–1 1–3 3–6 6–12 1–1.9 1.9–2.8 2.8–3.6 3.6–4.3 4.3–5.7 5.7–7.3 7.3–9.3 9.3–10.6 10.6–12 12–20 >20
USD
10-yr swap (100) 100
fixed receiver
Weight (%) 0.00 0.20 0.40 0.70 1.25 1.75 2.25 2.75 3.25 3.75 4.50 5.25 6.00 8.00 12.5
Postion × weight
long 3.75
short (0.20)
Vertical
disallowance
Horizontal 0 × 40% = 0 0 × 30% = 0 0 × 30% = 0
disallowance 1
Horizontal 0 × 40% = 0 0 × 40% = 0
disallowance 2
Horizontal 0.2 × 100% = 0.20
disallowance 3
Overall 3.55 × 100% = 3.55
net position
Total capital charge for general market risk = 3.75
(table continued on next page)

Page 171
(table continued from previous page)
Portfolio 2 Zone 1 (months) Zone 2 (years) Zone 3 (years)
Time band
Coupon >3% 0–1 1–3 3–6 6–12 1–2 2–3 3–4 4–5 5–7 7–10 10–15 15–20 >20
Coupon <3% 0–1 1–3 3–6 6–12 1–1.9 1.9–2.8 2.8–3.6 3.6–4.3 4.3–5.7 5.7–7.3 7.3–9.3 9.3–10.6 10.6–12 12–20 >20
Positions
A (100) 100
B 100 (100)
Weight (%) 0.00 0.20 0.40 0.70 1.25 1.75 2.25 2.75 3.25 3.75 4.50 5.25 6.00 8.00 12.5
Postion × weight
long .20 3.75
short (.20) (2.75)
Vertical disallowance 0.20 × 10% = 0.02
Horizontal 0 × 40% = 0 0 × 30% = 0 2.75 × 30% = 0.825
disallowance 1
Horizontal 0 × 40% = 0 0 × 40% = 0
disallowance 2
Horizontal 0 × 100% = 0
disallowance 3
Overall net position 1 × 100% = 1
Total capital charge for general market risk = 1.845

Page 172
Table 4.15
Standardized versus Internal Models: Capital Charge for Portfolios 1 and 2
Portfolio 1 Portfolio 2
(in USD) (in USD)
Internal model
(1) VaR = 927,000 407,532
= 8,794,294 3,866,188
(2) General market risk:
(3) Counterparty risk* (1988 Accord) = 60,000 120,000
Capital charge: (2) + (3) = 8,854,294 3,986,188
Standardized approach
(4) General market risk (cf. Table 4.14) = 3,750,000 1,845,000
(5) Counterparty risk* (1988 Accord) = 60,000 120,000
Capital charge: (4) + (5) = 3,810,000 1,965,000
Capital addition** = 132% 103%
* Details for the calculation of the capital charge for counterparty risk:
• Replacement cost = 0 (at-the-money swap)
• Add-on (cf. Table 4.4) = $ 100m × 1.5% = $1,500,000
• Risk-weighted amount (cf. Table 4.2) = $1,500,000- × 50% = $750,000-
• Capital charge = $750,000 × 8% = $60,000
** Capital addition (saving) is the addition (saving) of capital realized by the bank by adopting the internal models
instead of the standardized approach.
Table 4.16
Standardized versus Internal Models: Capital Charge for Portfolios 3 and 4
Portfolio 3 Portfolio 4
(in USD) (in USD)
Internal model
(1) VaR = 19,068 970,330
= 180,898 9,205,390
(2) General market risk:
(3) Counterparty risk (swap) (1988 Accord) = 60,000 166,800***
Capital charge: (2) + (3) = 240,898 9,372,190

Standardized approach
(4) General market risk* = 575,000* 10,425,000**
(5) Counterparty risk (1988 Accord) = 60,000 166,800
Capital charge: (4) + (5) = 635,000 10,591,800
Capital saving = 62% 11.5%
* The derivation is left to the reader. The capital charge is made of 375,000 USD for basis risk and 200,000 USD
for the overall net outright position. Obviously, for this portfolio the standardized approach appears to be
excessively onerous, while the VaR is small as the portfolio is relatively hedged.
** According to the standardized approach the CAD swap has a capital charge of 5,250,000 CAD while it is
3,750,000 USD for the U.S. swap, i.e., 5,175,500 CAD.
*** The capital charge for the U.S. swap is 60,000 USD, i.e., 82,800 CAD assuming an exchange rate of 1 USD =
1.38 CAD. The capital charge for the CAD swap is 84,000 CAD.

Page 173
Table 4.17
Internal Model for Portfolio 4
CAD SWAP USD SWAP
DV01 Volatility VaR DV01 Volatility VaR
Term (CAD) (bp) (σ) (CAD) (USD) (bp) (σ) (USD)
On 0 10.40 0 0 30.23 0
1m 0 4.63 0 0 6.30 0
2m (161) 4.07 1,523 0 3.91 0
3m (3,300) 5.09 39,150 2,459 3.59 20,588
6m 131 6.67 2,042 (28) 3.35 215
9m 196 7.16 3,264 (123) 3.46 988
1y 250 7.64 4,446 (162) 3.58 1,350
1.25y 307 8.11 5,796 (195) 3.95 1,794
1.5y 362 8.58 7,230 (230) 4.33 2,319
1.75y 433 9.05 9,124 (264) 4.70 2,894
2y 1,152 9.51 25,541 (746) 5.08 8,824
3y 2,614 9.13 55,584 (1,681) 5.29 20,742
4y 3,253 8.63 65,407 (2,092) 5.50 26,808
5y 5,551 8.14 105,280 (3,579) 5.50 45,897
7y 11,049 7.55 194,397 (7,308) 5.63 95,878
10y 73,161 7.00 1,193,291 (58,138) 5.42 734,252
15y 0 6.39 0 0 5.44 0
20y 0 6.07 0 0 5.07 0
30y 0 5.79 0 0 5.18 0
Exchange rate 1 USD = 1.38 CAD
VaR USD-Swap = 1,279,000 CAD
VaR USD-Swap = 1,626,000 CAD
VaR of Portfolio 4 = 970,330 CAD
With this capital attribution infrastructure and those risk measurement tools in place, the focus is gradually shifting
toward performance measurement. The board and top management of financial institutions are moving towards
compensation systems that are based on adjusted return on economic capital—an approach also known as RAROC
(risk adjusted return on capital). This new paradigm will spark further research in the integration of market risk, credit
risk, and other types of risks such as operational risk.

Page 174
Table 4.18
Standardized versus Internal Models for Portfolio 5 Capital Charges for General Market Risk
Internal model
VaR for the CAD position = 408,350 CAD
VaR for the USD position = 425,660 CAD
VaR for Portfolio 5 = 662,610 CAD
= 6,286,078 CAD
Capital charge
Standardized approach
CAD position 3,570,000 CAD
USD position 9,239,100 CAD
Total = 12,809,100 CAD
Capital savings = 51%
We can also expect the regulatory environment to evolve in the future toward a generalized use
of internal models across all types of risks, provided data are available to support the models.
Notes
1. In Canada, only the maturity method is allowed by the regulator, OSFI. The duration
approach differs only by its more accurate method of calculating the sensitivities, or risk
weights (see Table 4.2).
2. See Chapter 5. Delta represents the first-order approximation of the sensitivity of an option
value to a change in the underlying price.
3. See Chapter 5. Gamma denotes the second-order adjustment of the sensitivity of an option
value to a change in the underlying price. It is also the sensitivity of delta to a change in the
underlying price.
4. A Taylor expansion of a function designates its polynomial approximation, which agrees
with the value of the function and some of its derivatives at a given point, say the price of the
underlying instrument (see Apostol 1967.)
5. It is valued at current spot exchange rates, since we are interested in the present value of the
forward exposures.
6. Each of the seven provinces in Canada issues its own debt, which is not guaranteed by the
government of Canada. As a consequence

Page 175
provincial debts trade at a spread above the government debt of Canada, and the spread varies
from one province to another.
7. The convenience yield for commodities, like energy products, reflects the benefits from direct
ownership of the physical commodity, e.g., when there is a risk of shortage. It is affected by market
conditions as well as specific conditions such as the level of inventory and storage costs.
Accordingly, the convenience yield may be positive or negative. When inventory is high, demand is
low, and marginal storage costs are high, the convenience yield is likely to be negative.
8. When assessing the risk of a position, we are only focussing on the ''downside" risk, i.e., the risk of
a loss that is contained in the left tail of the distribution.
9. The square root of 10 rule is only valid when the changes in the portfolio values are not correlated
and are identically distributed.
10. If historical data are weighted to estimate volatilities and correlations, the weighted average time
lag of the individual observations should be at least half a year, which is what would be obtained if
the observations were equally weighted.
11. From the previous section we know that under the standardized approach, specific risk charges
vary across debt and equity instruments, with individual equities receiving 8 percent charges, while
those held in well-diversified and liquid portfolios are charged at 4 percent. Major stock indices are
subject to 2 percent charges and certain arbitrage positions receive lower requirements. For bonds,
specific risk charges vary between 0 percent and 8 percent depending on the issuer and the maturity
of the instrument, but no diversification is recognized.
12. See ISDA (1996) and IIF (1996). ISDA (1996) sets out the conclusions of a joint task force of
members of the International Swaps and Derivatives Association (ISDA) and the London Investment
Banking Association (LIBA) on aspects of the Basle Committee's standards for the use of the internal
models to calculate market risk capital charge. IIF (1996) reports the conclusions on the specific risk
issue of a task force composed of the representatives of 15 banks that were members of the Institute
of International Finance (IFF).
13. See Sharpe and Alexander (1990), Chapter 8.
14. The limits on the capital used vary slightly from one country to the other. For example, OSFI in
Canada limits the use of tier 2 and tier 3 capital to meet market risk requirements to 200 percent of
tier 1

Page 176
capital used to meet these requirements. In addition, tier 1 and tier 2 capital cannot, in total,
exceed 100 percent of tier 1 capital.
15. VaR is an assessment of the potential loss for a given, static portfolio, i.e., the closing position at
the end of the day. Obviously, the portfolio is traded all the time, so its composition continues to
change during the trading day. Risk management is also active, and decisions to alter the risk
exposure of the bank's position may be taken during the course of the day. This is why VaR should
be compared ex-post to these two measures of P&L.
16. Indeed, a 99 percent one-tail confidence level means that we expect losses, but also profits, to be
greater than VaR in absolute value 2.5 days per year.
17. The obligation to back-test was effective only after a year, i.e., in 1999, after institutions had
accumulated one year of historical market data to be used in back-testing. Initially, during 1998, the
regulators required only a comparison of VaR against actual P&L.
From our point of view, a better approach to back-testing would be "historical simulation" where,
each day, the position would be re-evaluated based on the last 250 days closing market data.
Then, the "historical distribution" of the changes in the position value would be compared with
the "theoretical distribution" derived from the internal VaR model. This approach would permit
one, over time, to revisit the key assumptions made in the VaR model which, through historical
simulation, are revealed to be inconsistent with market data—and which might produce a very
biased picture of the bank's exposure.
18. See Kupiec and O'Brien (1995c, 1995d, and 1996).
19. See Kupiec and O'Brien (1997).
20. For reasons of space, we do not present the relevant correlation matrix.
21. The VaR methodology for market risk is presented in Chapter 5.

Page 177
Chapter 5—
Measuring Market Risk:
The VaR Approach
1—
Introduction
As discussed in Chapter 2, the original purpose of the 1988 BIS Accord was to impose minimum
capital requirements for credit risk. More recently, the 1996 Amendment (BIS 1998) extended the
Accord to incorporate market risk arising from the trading book of financial institutions. This chapter
discusses what is meant by the term market risk, and then describes the most widely accepted
methodology for modeling this risk: the value-at-risk (VaR) approach.
Put simply, "market risk" is the risk that changes in financial market prices and rates will reduce the
value of a security or a portfolio. In trading activities, risk arises both from open (unhedged) positions
and from imperfect correlations between market positions that are intended to offset one another.
Market risk is given many different names in different contexts. For example, in the case of a fund,
the market risk is often measured relative to a benchmark index or a portfolio, and is therefore
referred to as "risk of tracking error."
As discussed in Chapter 1, there are four major types of market risk:
Interest rate risk—The simplest form of interest rate risk is the risk that the value of a fixed-income
security will fall as a result of

Page 178
a change in market interest rates. Open positions arise most often from differences in the maturities,
nominal values, and reset dates of instruments and cash flows that are assetlike (i.e., "longs") and
those that are liabilitylike (i.e., "shorts").
The exposure that such differences, or "mismatches," generates depends not only on the amount held
and each position's sensitivity to interest rate changes, but also on the degree to which these
sensitivities are correlated within portfolios and, more broadly, across trading desks and business
lines.
Imperfect correlation between offsetting instruments, both across the yield curve and within the same
maturity for different issuers, can generate significant interest rate exposures. Although they may be
intended to produce a hedged portfolio, offsetting positions that have different maturities may leave
the portfolio holder exposed to imperfect correlations in the underlying reference rates. Such "curve"
risk can arise in portfolios in which long and short positions of different maturities are effectively
hedged against a parallel shift in yields but not against a change in the shape of the yield curve.
Parallel shifts occur when a shock in the market has an equal effect on yields with different maturity
dates; the yield curve is said to change shape when a shock in the market has a stronger effect on, say,
the returns of shorter-dated instruments than it has on the returns of longer-dated instruments.
Alternatively, even where offsetting positions have the same maturity, "basis" risk can arise if the
rates of the positions are imperfectly correlated. For example, three-month Eurodollar instruments
and three-month Treasury bills both naturally pay three-month interest rates. However, these rates are
not perfectly correlated with each other, and spreads between their yields may vary over time. As a
result, a three-month Treasury bill funded by three-month Eurodollar deposits represents an imperfect
offset or hedged position.
Price risk for fixed-income products can be decomposed into a "general market" risk component and
a "specific" risk component. Specific risk is the idiosyncratic component of the financial transaction,
and in this sense it is akin to the credit risk that is analyzed in Chapters 8 to 10.
Equity price risk—The price risk associated with equities also has two components. "General market
risk" refers to the sensitivity of an instrument or portfolio value to a change in the level of

Page 179
broad stock market indices. "Specific" or "idiosyncratic" risk refers to that portion of a stock's price
volatility that is determined by characteristics specific to the firm, such as its line of business, the
quality of its management, or a breakdown in its production process. A well-known result of portfolio
theory is that general market risk cannot be eliminated through portfolio diversification, while
specific risk can be diversified away.
Foreign exchange risk—The major sources of foreign exchange risk are imperfect correlations in the
movement of currency prices and fluctuations in international interest rates. As with all other market
risks, foreign exchange risk arises from open or imperfectly hedged positions. Although it is
important to acknowledge exchange rates as a distinct market risk factor, the valuation of foreign
exchange transactions requires knowledge of the behavior of domestic and foreign interest rates, 1 as
well as of spot exchange rates. Foreign exchange risk is one of the major risks faced by large
multinational corporations. Foreign exchange volatility can sweep away the return from expensive
investments, and at the same time place a firm at a competitive disadvantage vis- -vis its foreign
competitors.2 It may also generate huge operating losses and inhibit investment.3
Commodity price risk—The price risk of commodities differs considerably from interest rate and
foreign exchange risk, since most commodities are traded in markets in which the concentration of
supply can magnify price volatility. Moreover, fluctuations in the depth of trading in the market (i.e.,
market liquidity) often accompany and exacerbate high levels of price volatility. Therefore,
commodity prices generally have higher volatilities and larger price discontinuities—i.e., moments
when prices leap from one level to another—than most traded financial securities.
2—
Measuring Risk:
A Historical Perspective
The measurement of risk has changed over time. It has evolved from simple indicators, such as the
face value or "notional" amount for an individual security, through more complex measures of price
sensitivities such as the duration and convexity of a bond, to the latest methodologies for computing
VaR numbers (Figure 5.1). Each measure has tended at first to be applied to individual securities,

Page 180
Figure 5.1
Traditional Measures of Market Risk
and then to be adapted to measure the risk of complex portfolios such as those that contain
derivatives.
The quest for better and more accurate measures of market risk is ongoing; each new market turmoil
reveals the limitations of even the most sophisticated measures of market risk. This said, VaR is
proving to be a very powerful way of assessing the overall risk of trading positions over a short
horizon, such as a 10-day period, and under "normal" market conditions. In effect, the methodology
allows us to capture in a single number the multiple components of market risk we introduced in the
previous section (curve risk, basis risk, volatility risk, etc.). For example, bond prices fall when
interest rates rise according to a nonlinear relationship. Given a measure of the volatility of market
yields, and their correlations, the market risk of a bond portfolio can be represented as a VaR number.
VaR is less reliable as a measure over longer time periods. The danger posed by exceptional market
shocks, 4 which are often accompanied by a drying up of market liquidity, can only be captured by
means of supplemental methodologies such as stress testing and scenario analysis.

Page 181
2.1—
The Notional Amount Approach
Until recently, trading desks in major banks were allocated economic capital by reference to notional
amounts. The notional approach measures risk as the notional, or nominal, amount of a security, or
the sum of the notional values of the holdings for a portfolio, as illustrated in Figure 5.2.
This method is flawed since it does not:
• Differentiate between short and long positions
• Reflect price volatility and correlation between prices
Moreover, in the case of derivative positions in the over-the-counter market, there are often very
large discrepancies between the true amount of market exposure, which is often small, and the
notional amount, which may be huge. For example, two call options on the same underlying
instrument with the same notional value, and the same maturity, with one option being in-the-money
and the other one out-of-the-money, have very different market values and risk exposures.
As another example, imagine a situation in which interest rate swaps are written with many different
counterparties, and where
Figure 5.2
The Notional Amount Approach

Page 182
some of these swaps are being used to hedge the market risk exposure created by the others. In this
instance, simply adding up the notional amounts of the deals gives a misleading picture of the
portfolio market risk—though it provides some indication of the overall credit risk exposure.
2.2—
Factor Sensitivity Measures
Measures of factor sensitivity capture the sensitivity of an instrument or portfolio to changes in the
value of primary risk factors such as interest rates, yield to maturity, volatility, stock price, stock
index, etc. Risk factors are said to be primary when their dynamics, or behavior, are specified
externally to the measurement model. 5
For fixed-income products, a popular risk measure among traders is "DV01," also known as "value
of an 01." 6 This describes the sensitivity of security prices to a one-basis-point (bp) parallel shift in
the yield curve, or to a 1-bp change in a specific rate. This measure is consistent with the
conventional "duration" analysis of a bond, as described in Appendix 1. For small parallel shifts of
the yield curve, the price sensitivity of a fixed-income product can be approximated by a linear
function of the change in yield (see relation A9 in Appendix 1):
where:
P denotes the price of the security
y is the yield to maturity
dP/dy is the change in the security price for a change in the yield to maturity
D is the Macaulay duration of the security7
D* is the modified duration (D* = D / (1 + y))
The longer the maturity of the bond, the higher its duration—and the more sensitive the price of the
bond to a change in yield (Figure 5.3).
The price-yield relationship for a bond is nonlinear, which means that duration is only a first-order
approximation of the impact of a change in yield on the price. As shown in Appendix 1, a

Page 183
Figure 5.3
Interest Rate Sensitivity Measures: Value of an "01"
more accurate approximation is provided by the second-order expansion of the bond price formula
(see relation A13):
where CX denotes the convexity of the bond.
• For a portfolio of instruments priced from the same yield curve, price sensitivities can be easily
aggregated by calculating the weighted average duration of the instruments held in the portfolio.
• Alternatively, price sensitivities can be expressed in terms of one representative instrument, e.g., the
four-year Treasury note (T-note) in Figure 5.3. In this case, each position is converted into the
duration equivalent of the reference instrument, i.e., the four-year T-note. For instance, the 10-year T-
note has a duration that is 2.1 times greater than the duration of a four-year T-note, so a $1 million
10-year T-note is said to be equivalent to $2.1 million dollar of the reference four-year T-note (Figure
5.4). The risk of the portfolio is then evaluated as if it were a single position in the reference asset.

Page 184
Figure 5.4
Interest Rate Sensitivity Measures: Relative Value of an "01"
2.3—
Other Price Sensitivity Measures
Practitioners in the derivative markets have developed their own specialized risk measures. They refer to the sensitivities
of derivative instruments to various risk factors using a set of measures named after letters in the Greek alphabet, and
therefore known collectively as the "Greeks." How do these measures relate to the risk measures we have just discussed?
First, let us look again at the Black-Scholes (1973) formula (3), which represents the value, C, of a European call option on
an individual stock that does not pay any dividend: 8
where
S = the stock price which is assumed to follow a log-normal distribution
K = the strike price
N(.) = the cumulative standard normal distribution
r = the continuously compounded risk-free rate of interest which is assumed to be a
constant

Page 185
σ2 = the instantaneous variance of the stock return, assumed to be a constant
T = the time to maturity of the option
d1 =
d2 =
The stock price, S, in the option price equation (3), plays the same role as the yield, y, in the bond
price equation (A4) shown in Appendix 1. The sensitivities of the call option price with respect to
the price of the underlying instrument, S, are known as the delta and gamma. The delta and gamma
price risks of a derivative are analogous to the duration and convexity of a bond, respectively.
Table 5.1 describes the relationships between the Greeks in more detail, and presents their
mathematical representations.
The list of sensitivities for derivatives in Table 5.1 is longer than a similar list for a standard bond.
This is because the value of a derivative is affected by other risk factors such as volatility, σ, the
discount rate, r, the passage of time, t, and, when several risk factors are involved, the correlation
between the risk factors, ρ.
In the Greek formula, above, the expression
denotes the density function of the univariate standard normal distribution.
2.4—
Weaknesses of the Greek Measures
Each of the sensitivities measured by the Greeks provides only a partial measure of financial risk.
The measurements of delta, gamma, and vega complement each other, but they cannot be
aggregated to produce an overall measure of the risk generated by a position or a portfolio. In
particular:
• Sensitivities are not additive across risk types; e.g., the delta and gamma risk of the same position
cannot be summed.
• Sensitivities are not additive across markets; e.g., one cannot sum the delta of a Euro/$US call
and the delta of a call on a stock index.

Page 186
TABLE 5.1
The Greek Alphabet for a European Equity Call Option1
Delta, or price risk Delta measures the degree to which an option's value is affected by a small
change in the price of the underlying instrument.
Gamma, or convexity risk Gamma measures the degree to which the option's delta changes as the
reference price underlying the option changes. The higher the gamma, the
more valuable the option is to its holder. For a high gamma option, when the
underlying price increases, the delta also increases, so that the option
appreciates more in value than for a gamma neutral position. Conversely,
when the underlying price declines, the delta also falls, and the option loses
less in value than if the position was gamma-neutral. The reverse is true for
short positions in options: high gamma positions expose their holders to
more risk than gamma-neutral positions.
Vega, or volatility risk Vega measures the sensitivity of the option value to changes in the volatility
of the underlying instrument. A higher vega typically increases the value of
the option to its holder.
Theta, or time decay risk Theta measures the time decay of an option. That is, it reflects how much the
value of the option changes as the option moves closer to its expiration date.
Positive gamma is usually associated with negative time decay, i.e., a natural
price attrition of the option as its maturity declines.
Rho, or discount rate risk Rho measures the change in value of an option in response to a change in
interest rate, more specifically a change in the zero-coupon rate of the same
maturity as the option. Typically, the higher the value of rho, the lower the
value of the option to its holder.
1 For a detailed analysis of the Greeks for various types of options see Hull (2000).

Page 187
Since the sensitivities cannot be aggregated, they cannot be used to assess the magnitude of the
overall loss that might arise from a change in the risk factors. As a consequence:
• Sensitivities cannot be used directly to measure capital at risk.
• Sensitivities do not facilitate risk control. Position limits expressed in terms of delta, gamma, and
vega are often ineffective since they do not translate easily into a ''maximum loss acceptable" for the
position.
This explains the desire for a comprehensive measure of risk for individual securities and for
portfolios. Value-at-risk (VaR) is one answer to this quest for a consistent measure of risk.
3—
Defining Value at Risk
Value at risk 9 can be defined as the worst loss that might be expected from holding a security or
portfolio over a given period of time (say a single day, or 10 days for the purpose of regulatory capital
reporting), given a specified level of probability (known as the "confidence level").
For example, if we say that a position has a daily VaR of $10 million at the 99 percent confidence
level, we mean that the realized daily losses from the position will, on average, be higher than $10
million on only one day every 100 trading days (i.e., two to three days each year).
VaR is not the answer to the simple question:
How much can I lose on my portfolio over a given period of time?
The answer to this question is "everything," or almost the entire value of the portfolio! This answer is
not very helpful in practice. It is the correct answer to the wrong question. If all markets collapse at
the same time, then naturally prices may plunge and, at least in theory, the value of the portfolio may
drop near to zero.
Instead, VaR offers a probability statement about the potential change in the value of a portfolio
resulting from a change in market factors, over a specified period of time. VaR is the answer to the
following question (Figure 5.5):
What is the maximum loss over a given time period such that there is a low probability, say a 1 percent probability,
that the actual loss over the given period will be larger?

Page 188
Figure 5.5
Defining Value at Risk
Note that the VaR measure does not state by how much actual losses will exceed the VaR figure; it
simply states how likely (or unlikely) it is that the VaR figure will be exceeded.
Most VaR models are designed to measure risk over a short period of time, such as one day or, in the
case of the risk measurements required by the regulators to report regulatory capital, 10 days. BIS
1998 imposes a confidence level, c, of 99 percent. 10 However, for the purposes of allocating internal
capital, VaR may be derived at a higher confidence level, say c = 99.96 percent, which is consistent
with an AA rating.11
As illustrated in Figure 5.5, calculating VaR involves the following steps: First, derive the forward
distribution of the portfolio, or alternatively the returns on the portfolio, at the chosen horizon, H (of,
say, one day or 10 days). As we describe below, the distribution can be derived directly from
historical price distributions (nonparametric VaR) or the distributions may be assumed to be analytic;
e.g., it is common practice to assume that prices are log-normally distributed, or equivalently that
returns follow a nor-

Page 189
mal distribution (parametric VaR). Second, assuming that the confidence level, c, is 99 percent,
calculate the first percentile of this distribution; if the confidence level is 99.96 percent, then
calculate the 4-bp quantile.
The VaR is the maximum loss at the 99 percent confidence level, measured relative to the expected
value of the portfolio at the target horizon, i.e., VaR is the distance of the first percentile from the
mean of the distribution. 12
An alternative definition of VaR is that it represents the worst case loss at the 99 percent confidence
level:
VaR' is also known as "absolute VaR." Only the first definition (4) of VaR is consistent with
economic capital attribution and RAROC calculations (see Chapter 14). Indeed, in VaR the expected
profit/loss is already priced in, and accounted for, in the return calculation. Capital is provided only
as a cushion against unexpected losses.
Note that VaR relates to the economic capital that shareholders should invest in the firm to limit the
probability of default to a given predetermined level, 1–c, while regulatory capital is the minimum
amount of capital imposed by the regulator (Chapter 2). Economic capital differs from regulatory
capital because the confidence level and the time horizon chosen are different. Most of the time,
banks choose a higher confidence level than the 99 percent set by the regulator to determine their
economic capital. However, the time horizon in economic capital calculations may vary from one day
for very liquid positions, such as a government bond desk, to several weeks for illiquid positions,
such as a long-dated OTC equity derivatives portfolios. By contrast, the regulator arbitrarily sets the
time horizon to 10 days for any position in the trading book.
More formally, if V denotes the current marked-to-market value of the position, R is the return over
the horizon H, µ is the expected return [µ = E(R)], and R* denotes the return corresponding to the
worst case loss at the c, e.g., 99 percent, confidence level,

Page 190
so that if V* = V (1 + R*), then:
and
13
Example:
V = 100, µ = 5 percent and R* = –20 percent, then VaR = 100 (0.05 – (–0.20)) = 25 and VaR' = 20.
Note that R* is negative so that VaR is the sum of the absolute value of the worst case loss and of the
expected return. If the expected return happens to be an expected loss, then VaR is the difference
between the absolute values of the worst case loss and the expected loss. For example, if µ = –5
percent, then VaR = 100(–0.05 – (–.20) = 15 and VaR' = 20.
3.1—
Nonparametric VaR
Nonparametric VaR is derived from a distribution that is constructed using historical data. It is called
nonparametric VaR because, unlike the parametric approach described below, the calculation does
not involve estimating the parameters of a theoretical distribution. In the illustrative example in
Figure 5.6, the average daily pure net trading related revenue (e.g., net of fees) for CIBC during 1998
was C$0.451 million. The first percentile of the distribution, i.e., the cutoff point on this distribution,
such that only 1 percent of the daily revenues lie on its left-hand side, is C$–25.919 million.14
This means that VaR = 0.451 – (–25.919) = C$26.370M, and VaR' = C$25.919M.
3.2—
Parametric VaR
In the previous example, VaR was derived from the empirical distribution (histogram) of the daily
revenues generated by the position over a one-year period. No assumption was made about the
distribution of the returns of the position.

Page 191
Figure 5.6a
CIBC Net Daily Trading Revenues During 1998 versus One-Day VaR at the 99 Percent
Confidence Level
Figure 5.6b
CIBC Net Daily Trading Revenues for 1998 (CAD Millions)

Page 192
To simplify the derivation of VaR we may choose to assume that the returns have an analytic
density function, f(R). Historical data are used to estimate the parameters of the assumed
distribution function.
3.2.1—
Normal Return Distribution
For example, if R is normally distributed with mean, µ, and standard deviation, σ, then:
If c denotes the confidence level, say 99 percent, then R* is defined analytically by the
following expression:
Z = (R – µ)/σ denotes a standard normal variable, N(0,1), with mean 0 and unit standard
deviation. In the case of normal returns, the derivation of R* becomes very simple and relies
only on the published tables of the standard cumulative normal distribution. The threshold
limits, α, for various confidence levels are given in Table 5.2.
The cut-off return R* can be expressed as:
TABLE 5.2
Threshold Limits, α, as a Function of the
Confidence Level
c
99.97% –3.43
99.87% –3.00
99% –2.33
95% –1.65

Page 193
From the definition (6) of VaR and (7) of absolute VaR', it follows that:
3.2.2—
Student-t Return Distribution
There is a large amount of evidence that many individual return distributions are not normally
distributed, and exhibit what are known as "fat tails." The term "fat tails" arises out of the shape of
certain distributions when plotted on a graph. In these distributions, there are more observations far
away from the mean than is the case in a normal or bell-shaped distribution. So whereas a normal
distribution tails off quickly to reflect the rarity of unlikely events, the tail of a fat-tailed distribution
remains relatively thick (e.g., Campbell, Lo, and MacKinlay, 1997).
Fat tails in distributions are particularly worrying to risk managers because they imply that
extraordinary losses occur more frequently than a normal distribution would lead us to believe.
Luckily, even if the returns of an individual factor do not follow a normal distribution, the returns of a
well-diversified portfolio across many different risk factors might still exhibit a normal distribution.
This effect is explained by the central limit theorem, which tells us that the independent random
variables of well-behaved distribution will possess a mean that converges, in large samples, to a
normal distribution.
In practice, this result implies that a risk manager can assume that a portfolio has a normal returns
distribution, provided that the portfolio is fairly well diversified and the risk factor returns are
sufficiently independent from each other (even when they are not themselves normally distributed).
If it is felt that the normal distribution is inadequate for describing the portfolio returns, 15 one can
use as an alternative the class of Student-t distributions. As illustrated Figure 5.7, these distributions
allow for fat tails and, at the same time, produce derivations as tractable as those produced by the
normal distribution.
The Student-t distribution is fully characterized by the mean, µ, and the variance, σ2, of the portfolio
return, and by an additional

Page 194
Figure 5.7
Comparison of the Unit Normal and Student-t Distributions
parameter called the "degree of freedom," ν, that controls the fatness of the tail, i.e., the degree of
leptokurtosis. 16 The smaller ν, the fatter the tails of the Student-t distribution. As ν gets larger, the
distribution converges to the normal distribution with mean, µ, and variance, σ2. According to Jorion
(1995), ν varies in the range 4 to 8 for most financial time series.
We would expect the VaR derived from a Student-t distribution to be higher than that derived from a
normal distribution. To find VaR when the portfolio return is distributed according to a Student-t
distribution, simply replace f(R) in equation (8) with the appropriate Student-t distribution. For
example, when ν is equal to 5, VaR at the 99 percent confidence level is 3.365 standard deviations,
instead of 2.33 when the distribution is normal.
3.3—
From 1-Day VaR to 10-Day VaR
When VaR is used to manage risk on a daily basis, then one-day VaR is needed. One-day VaR must
be derived from the daily distribution of the portfolio values. However, 10 days is the time horizon
set by the regulators for the purpose of reporting regulatory

Page 195
capital. Ideally, the 10-day VaR should be derived from the corresponding distribution over a 10-day
horizon. However, can one also derive the 10-day VaR, or the VaR over any other time horizon, from
the daily VaR?
If we assume that markets are efficient and daily returns, Rt, are independent and identically
distributed (i.i.d.), then the 10-day return, , is also normally distributed with mean
µ10 = 10µ, and variance , since it is the sum of 10 i.i.d. normal variables. It follows that:
This means that the 10-day VaR can be approximated by multiplying the daily VaR by the square
root of time (here, 10 days). This result would not hold if the stock returns exhibit mean reversion, are
serially correlated, or more generally are not i.i.d. 17
3.4—
VaR Is for Managing, as Well as Measuring, Risk
To implement the VaR methodology, analysts must make simplifying assumptions. We discuss the
problems and limitations inherent in those assumptions below. But first, let us stress that VaR is a
powerful approach and has far-reaching uses:
• VaR provides a common, consistent, and integrated measure of risk across risk factors, instruments,
and asset classes, leading to greater risk transparency and a consistent treatment of risks across the
firm. For example, it allows managers to measure the risk of a fixed-income position in a way that is
comparable and consistent with their risk assessment of an equity derivative position. VaR also takes
account of the correlations between the various risk factors. If two risks offset each other, VaR allows
for this offset and tells us that the overall risk is relatively small. If, on the contrary, one risk
increases another risk, then VaR takes this into account and produces a higher risk estimate. In other
words, VaR measures risk in a portfolio framework somewhat in the spirit of portfolio theory.
• VaR provides an aggregate measure of risk: a single number that is related to the maximum loss that
might be incurred on a position, at a given confidence level. This single number can then be easily
translated into a capital requirement. VaR can also be used

Page 196
to reward employees on the basis of the risk-adjusted return on capital generated by their activities. In
other words, it can be used to measure risk-adjusted performance (see Chapter 14). VaR can therefore
be used to discourage risk taking that does not add value from the shareholder's perspective.
• The risks taken by the business line can be monitored using limits set in terms of VaR. These limits
can be used to ensure that individuals do not take more risk than they are allowed to take. Risk limits
expressed in VaR units can easily be aggregated up through the firm: from the business line, at
trading desk level, to the very top of the corporation. The drill-down capability of a VaR system
allows risk managers to detect which unit is taking the most risk, and also to identify the type of risk
to which the whole bank is most exposed, e.g., equity, interest rate, currency, credit spread, equity
vega, etc. 18
• VaR provides senior management, the board of directors, and regulators with a risk measure that
they can understand. Managers and shareholders, as well as regulators, can decide whether they feel
comfortable with the level of risk taken on by the bank in terms of VaR units. VaR also provides a
framework to assess, ex ante, investments and projects on the basis of their expected risk-adjusted
return on capital.
• A VaR system allows a firm to assess the benefits from portfolio diversification within a line of
activity, but also across businesses (such as the equity and fixed-income businesses). It allows
managers to assess the daily revenue volatility they might expect from any given trading area.
• VaR has become an internal and external reporting tool. VaR reports are produced daily for
managers of business lines, and are then aggregated for senior management. VaR is also
communicated to the regulators, and has become the basis for calculating regulatory capital. The
rating agencies take VaR calculations into account in establishing their rating of banks. Increasingly,
VaR is also published in banks' annual reports as a key indicator of risk (Figure 5.6).
4—
Calculating Value at Risk
As we discussed, to calculate VaR we first need to generate the forward distribution of the portfolio
values at the risk horizon or,

Page 197
equivalently, the distribution of the changes in the value of the portfolio. Only after this can we
calculate the mean and the quantiles of this distribution (Figure 5.5).
There are three approaches to deriving this distribution:
• The analytic variance-covariance approach
• The Monte Carlo approach
• The historical simulation approach
These all share the following two preliminary steps.
(i)—
Selection of the Risk Factors
The change in the value of the portfolio is driven by changes in the market factors that influence the
price of each instrument. The relevant risk factors depend on the composition of the portfolio. The
selection of risk factors is straightforward for a simple security, but it requires judgement for more
complex products.
In the case of a simple security, such as a $US/Euro forward, the value of the position is affected only
by the $US/Euro forward rate. In the case of a $US/Euro call option, the value of the position
depends not only on the $US/Euro exchange rate, but also on the dollar and the Euro interest rates
over the maturity of the option, as well as the $US/Euro volatility (Table 5.3).
The market factors that affect prices vary by instruments. In the case of a stock portfolio, the risk
factors are the prices of the individual stocks that compose the portfolio. For a bond portfolio, the
choice of the risk factors depends on the degree of ''granularity" that one needs to achieve. For
example, the risk factor for each bond might simply be its yield to maturity.
TABLE 5.3
Example of a Selection of Risk Factors
USD/Euro forward USD/Euro option
• USD/Euro forward rate • USD/Euro exchange rate
• USD interest rates
• Euro interest rates
• USD/Euro volatility

Page 198
Alternatively, it could be a selection of zero-coupon rates on the risk-free term structure of interest
rates for each currency. For example, the selection might comprise the overnight, the 1-month, 3-
month, 6-month, 1-year, 3-year, 5-year, 10-year, and 30-year zero-coupon rates, as well as the spread
in prices between different issuers for the same terms (so that the calculation captures issuer risk).
(ii)—
Choice of a Methodology for Modeling Changes in Market Risk Factors
The analytic variance-covariance approach assumes that the risk factors are log-normally distributed
or, equivalently, that their log-returns are normally distributed.
The historical simulation approach does not oblige the user to make any analytic assumptions about
the distributions. VaR is derived from the empirical distribution generated by the historical
realizations of the risk factors over a specified period of time. However, at least two or three years of
data are necessary to produce meaningful results.
The Monte Carlo methodology can be implemented by choosing any analytic multivariate
distribution for the risk factors. The only limitation is the ability to estimate the parameters of the
distribution, such as the means, the variances, and the covariances. The Monte Carlo methodology is
flexible and allows the analyst to choose distributions that exhibit fat tails and skewness (e.g.,
Student-t distributions). Processes with mean reversion can also be simulated. Complex distributions,
such as mixtures of normal distributions or the mixture of a normal and a jump process (alternative
ways to capture fat tails), can also be dealt with easily.
4.1—
Analytic Variance-Covariance, or "Delta-Normal," Approach:
Case of a Portfolio Linear in Risks 19
The analytic variance-covariance approach assumes that the distribution of the changes in the
portfolio value is normal.20 Since the normal distribution is completely characterized by its first two
moments, the analyst must simply derive the mean and the variance of this normal distribution from:

Page 199
• The multivariate distribution of the risk factors; and
• The composition of the portfolio.
The analytic approach is an extension of the portfolio model as pioneered by Markowitz (1952,
1959), and is illustrated in the following example.
Example 1—
Stock Portfolio
Consider a portfolio composed of two stocks, say Microsoft and Exxon, with n1 shares of Microsoft
valued at S1 per share, and n2 shares of Exxon valued at S2 per share. 21 Then, the value of the
portfolio is:
1—
Selection of the Risk Factors
The risk factors are the stock prices, S1, and S2, respectively. It follows that:
where
Rv = the rate of return on the portfolio
Ri = the rate of return on stock i, Ri ≡ ∆Si/Si
ωi = the percentage of the portfolio invested in stock i, i, = 1,2, with Σ wi = 1
2—
Distribution of the Risk Factors
Prices are assumed to be log-normally distributed, so that log-returns during the period (t – 1,t), i.e.,
are normally distributed, where St (St–1) denotes the price of the stock at time t (t – 1), and ∆S is the
price change during the period, ∆S = St – St–1.22

Page 200
More specifically, we assume that Ri = the rate of return on stock i, i = 1,2, follows a multivariate
normal distribution with mean, µi, and standard deviation, σi, and correlation coefficient ρ between
the rates of return on the two stocks.
3—
One-Day and 10-Day VaR Calculation for an Individual Stock
The marginal distribution for each stock return is univariate normal:
so that, according to (10) and (11), the one-day and 10-day VaRs at the 99 percent confidence level
are, respectively:
4—
One-Day and 10-Day VaR Calculation for the Stock Portfolio
The return on the portfolio, as defined in (14), being a linear combination of normal distributions, is
also normally distributed:
with
where w = (ω1 ω2) denotes the 1 2 weight vector, Ω is the variance-covariance matrix, σ is the 2
2 diagonal standard deviation matrix, C is the 2 2 correlation matrix and wT denotes the transpose
of w.

Page 201
Formula (16) is general, and applies to a portfolio that is linear in risks 23 with N risk factors, while
the dimensions of the vectors and matrices are adjusted accordingly. However, to reduce the
dimensionality of the correlation matrix, one can rely on the market model, also known as the "beta"
model, as shown in Appendix 3.
Then, according to (10) and (11), the one and 10-day VaRs for the portfolio at the 99 percent
confidence level are, respectively:
The expression (17) for VaR, using (16), can also be rewritten as:
where VaR denotes the 1 2 vector of individual VaRs for each stock position, i.e., VaR = [VaR1
VaR2] as specified in (15), adjusted for the number of shares.24
Expression (18) offers a convenient way of showing the impact of correlations on the overall VaR of
a portfolio. If stock returns are perfectly correlated, with the correlations equal to one, then VaRV is
simply the sum of the VaRs of the individual stocks that compose the portfolio. In that instance, there
is no diversification effect. When correlations are less than one, then VaRV is less than the sum of the
individual VaRs. The following numerical application illustrates the portfolio effect for different
values of the correlation coefficient.
Numerical Application
From historical data we estimate the simple historical mean and standard deviation of the daily
returns over a one-year period for two stocks, e.g., Microsoft and Exxon, denoted by S1 and S2,
respectively. We can also estimate the correlation coefficient, ρ, between their rates of return. As of
November 26, 1999, we obtain the one-day means and standard deviations based on the last 260
trading days:
Assume that the portfolio is composed of 100 shares of Microsoft and 120 shares of Exxon valued at
$91.7 and $79.1, respectively. Then, the value of the portfolio is:

Page 202
and the relative investments in both stocks are, respectively:
so that the one-day mean and standard deviation of the rate of return on the portfolio are:
The one-day VaRs at the 99 percent confidence level are:
where VaR1, VaR2, and VaRV denote the one-day value at risk at the 99 percent confidence level for
Microsoft, Exxon, and the portfolio, respectively. Note that VaRV (1; 99) = $677 is less than the sum
of VaR1(1; 99) and VaR2(1; 99), i.e., $887.
The difference, $210, represents the portfolio effect that results from the imperfect correlation
between the equity returns. VaR is in fact quite sensitive to the correlation structure of the risk
factors. Table 5.4 shows the sensitivity of VaR to the correlation coefficient for the previous equity
portfolio.
We can also derive the absolute VaR', i.e.:
Example 2—
A Zero-Coupon Bond
1. Consider a hypothetical position in a 10-year French zero-coupon "OAT" bond with a nominal
value of 100 million French francs (FRF).
The risk factor is the 10-year yield, y, whose current value is supposed to be y = 7.96 percent. It is
also assumed to be normally distributed with a daily volatility σ (y) = 9.63bp (or 0.0963 percent). It
follows that the price of the bond is B = 100/1.079610 = 46.491 million FRF.

Page 203
TABLE 5.4
VaR of a Stock Portfolio for Different Correlation Coefficients
ρ VaR (1;99) Portfolio Effect
–1.0 $887 $0
0.5 $772 $115
0 $636 $251
–0.5 $461 $426
–1.0 $146 $741
If we now assume that the change in the bond price is governed by the duration-based relation (1)
(Section 2.2), we have: 25
so that, dB is normally distributed with a daily volatility:
and:
2. Now, suppose that the French bond is held by a U.S. investor, for whom the risks should be
denominated in $US. Assume also that the exchange rate, e, is 5.402 FFR per $US, the daily
volatility of its log-return is σ(de/e) = 0.58 percent, and the correlation between the French yield and
the exchange rate is ρ(dy, de/e) = -0.0726. Then,
and

Page 204
Thus,
and
Note, from (20), that the change in the value of the bond expressed in $US is normally distributed, as
it is the weighted sum of two normal distributions. Then:
The risk of this position is reduced by a negative correlation between the yield of the French bond
and the exchange rate. If the correlation was +1 instead of -.0726, then the one-day VaR would be
$295,173. The portfolio effect associated with the imperfect correlation is:
4.2—
Delta-Normal VaR for Other Instruments
The previous analysis can be easily generalized to any type of financial instruments for which the
equilibrium value, V, can be expressed as a function of n risk factors, fi, i = 1, . . . , n. The change in
value, dV, can be approximated by a first-order Taylor expansion of the pricing equation, i.e.:

Page 205
where ∆i denotes the "delta" of the position in the instrument, i.e., the small change in V in response
to a small change in factor i. From (20) it follows that:
If we assume that the changes in the risk factors are normally distributed, the change in the asset
value, dV, is also normally distributed, so that:
In the following we illustrate the calculation of equation (21) for two simple derivatives: a forward
contract and an option. Once (21) has been derived, the calculation of VaR according to (22) becomes
straightforward. It only requires the variance and covariance statistics for the risk factors.
(i)—
Forward Contract 26
This is the simplest type of derivative contract. Under a forward agreement, the buyer is obliged to
take delivery of a given quantity of financial asset or commodity, at a prearranged date and price (the
forward price). The seller of the forward contract is also obligated to deliver under the same terms.
The forward price is set so that the value of the contract is zero at inception, and the value at time t of
the forward contract for the buyer is Ft:
such that:
St = current price of the security or commodity to be delivered
FT = forward price, i.e., delivery price
t, T = current time and delivery time (time when the forward contract matures), respectively
r = risk-free rate of interest with continuous compounding, for an investment maturing at
time T
y = continuous dividend yield paid out by the security, and assumed to be continuously
reinvested in the security27

Page 206
Equation (24) is derived from the no-arbitrage argument. 28 The investment in the underlying security
over the period (T, t) can be replicated by buying the existing forward contract at its current price, Ft,
and setting aside the present value of the contractual purchase price, FT. Then, the change in value of
the forward value expressed in terms of the changes in the risk factors St, r, and y, is:
(ii)—
Option Contracts
In Section 2.3, and in Chapter 1, we discussed the pricing of European call options on an individual
stock that does not pay any dividend, using the Black-Scholes formula (3):29
Then, according to the delta-normal approach to VaR, the change in value of the option can be
approximated using the "Greeks" (Table 5.1), by:
4.3—
Historical Simulation Approach
The historical simulation approach to VaR is conceptually simple. First, the changes that have been
seen in relevant market prices and rates (the risk factors) are analyzed over a specified historical
period, say, one to four years. The portfolio under examination is then revalued, using changes in the
risk factors derived from the historical data, to create the distribution of the portfolio returns from
which the VaR of the portfolio can be derived. Each daily simulated change in the value of the
portfolio is considered as an observation in the distribution.

Page 207
Three steps are involved:
• Select a sample of actual daily risk factor changes over a given period of time, say 250 days (i.e.,
one year's worth of trading days).
• Apply those daily changes to the current value of the risk factors and revalue the current portfolio as
many times as the number of days in the historical sample.
• Construct the histogram of portfolio values and identify the VaR that isolates the first percentile of
the distribution in the left-hand tail, assuming VaR is derived at the 99 percent confidence level. 30
We now illustrate the approach using an example.31 Assume that the current portfolio is composed of
a three-month $US/DM call option. The market risk factors for this position are:
• $US/DM exchange rate
• $US three-month interest rate
• DM three-month interest rate
• Three-month implied volatility of the $US/DM exchange rate
In the following we neglect the impact of the interest rate risk factors and only consider the level of
the exchange rate and its volatility. In this example we use daily observations over the past 100 days.
They are reported in columns 2 and 3 of Table 5.5.
Historical simulation, like Monte Carlo simulation, requires the repricing of the position using the
historical distribution of the risk factors.32 In this example we use the Black-Scholes model adapted
by Garman-Kholhagen (1983) to currency options (Table 5.6).
The last step consists of constructing the histogram of the portfolio returns based on the last 100 days
of history, or equivalently sorting the changes in portfolio values to identify the first percentile of the
distribution. Table 5.7 shows the ranking of the changes in value of the portfolio. Using this, we
identify the first percentile as–$0.07.
Figure 5.8 shows the histogram of these values. VaR (1; 99) at

Page 208
TABLE 5.5
Historical Market Values for the Risk Factors Over the Last 100
Days
Day $US/DM FX Volatility
(t) (FXt) (σt)
–100 1.3970 0.149
–99 1.3960 0.149
–98 1.3973 0.151
... ... ...
–2 1.4015 0.163
–1 1.4024 0.164
the 99 percent confidence level is simply the distance to the mean ($0.01) of the first percentile, i.e., VaR
(1;99) = $0.08, while absolute VaR is the first percentile itself, i.e., VaR' (1; 99) = $0.07.
This approach can easily be generalized to any portfolio of securities. The approach follows the same three-
step procedure. Select the relevant risk factors and gather the historical data using the same historical
period for all the factors. Calculate the changes in value for all the constituents of the portfolio, and sum up
these changes across all positions, for each day, keeping the days synchronized. Construct the histogram of
the portfolio returns, or
TABLE 5.6
Simulating Portfolio Values Using Historical Data (Current Value of the Portfolio: $1.80)
Change from Current Value
($1.80)
Alternate price 100 = C(FX100; σ100) = $1.75 –$0.05
Alternate price 99 = C(FX99; σ99) = $1.73 –$0.07
Alternate price 98 = C(FX98; σ98) = $1.69 –$0.11
.......
Alternate price 2 = C(FX2; σ2) = $1.87 +$0.07
Alternate price 1 = C(FX1; σ1) = $1.88 +$0.08

Page 209
TABLE 5.7
Identifying the First Percentile of the Historical Distribution of the
Portfolio Return
Rank Change from Current Value
100 –$0.11
99 –$0.07
98 –$0.05
... ...
2 +$0.07
1 +$0.08
equivalently sort the values to identify the first percentile of the distribution, assuming VaR is
derived at the 99 percent confidence level.
Below, we illustrate these steps with regard to a portfolio composed of the $US/DM call option
described above, and a German bond. 33
• Step 1: Risk factors and historical market values (Table 5.8)
• Step 2: Change in the value of the portfolio (Table 5.9)
Figure 5.8
VaR from Historical Simulations

Page 210
TABLE 5.8
Risk Factors and Historical Market Values
Day $US/DM FX Volatility German Interest Rate (%)
(t) (FXt) (σ t) (DMYTMt)
–100 1.3970 0.149 5.125
–99 1.3960 0.149 5.125
–98 1.3973 0.151 5.100
... ... ... ...
–2 1.4015 0.163 4.910
–1 1.4024 0.162 4.925
Note: The exchange rate and its volatility are reported in Table 5.5.
We have already discussed the pricing model for the foreign exchange call option. We use a
simple discount valuation model for the German bond, employing the German bond's yield to
maturity. This value in DM must then be translated into $US using the current exchange rate
(Table 5.9).
Today's $US price of the German bond:
TABLE 5.9
Changes in Portfolio Value
Change in $US/DM Change in German Change in Portfolio
Day Call Bond Value
–100 –$0.05 –$0.03 –$0.08
–99 $0.07 $0.02 –$0.05
–98 –$0.11 $0.15 +$0.04
... ... ... ...
–2 $0.07 –$0.12 –$0.05
–1 $0.08 –$0.02 –$0.06

Page 211
Figure 5.9
VaR from Historical Simulation for the Portfolio: USD/DM Call and German
Bond
• Step 3: Identify the first percentile of the portfolio return distribution (Figure 5.9).
The major attraction of historical simulation is that the method is completely nonparametric and does
not depend on any assumption about the distribution of the risk factors. We do not need to assume
that the returns of the risk factors are normally distributed and independent over time. 34
The nonparametric nature of historical simulation also obviates the need to estimate volatilities and
correlations. Historical volatilities and correlations are already reflected in the data set, and all we
need to calculate are the synchronous risk factor returns over a given historical period. Historical
simulation has also no problem accommodating fat tails, since the historical returns already reflect
actual synchronous moves in the market across all risk factors. Another advantage of historical
simulation over the variance-covariance approach is that it allows the analyst to calculate confidence
intervals for VaR.
The main drawback of historical simulation is its complete dependence on a particular set of
historical data—and thus on the idiosyncrasies of this data set. The underlying assumption is that the
past, as captured in the historical data set, is a reliable representation of the future. This implicitly
presumes that the market events embedded in the data set will be reproduced in the months to come.
However, the historical period may cover events such as

Page 212
a market crash or, conversely, a period of exceptionally low price volatility, that are unlikely to be
repeated in the future. Historical simulation may also lead to a distorted assessment of the risk if we
employ the technique regardless of any structural changes anticipated in the market—such as the
introduction of the Euro at the beginning of 1999.
Another practical limitation of historical simulation is data availability. One year of data corresponds
to only 250 data points (trading days) on average, i.e., 250 scenarios. By contrast, Monte Carlo
simulations usually involve at least 10,000 simulations (i.e., scenarios). Employing small samples of
historical data inevitably leaves gaps in the distributions of the risk factors and tends to
underrepresent the tails of the distributions, i.e., the occurrence of unlikely but extreme events.
4.4—
Monte Carlo Approach 35
Monte Carlo simulation consists of repeatedly simulating the random processes that govern market
prices and rates. Each simulation (scenario) generates a possible value for the portfolio at the target
horizon (e.g., 10 days). If we generate enough of these scenarios, the simulated distribution of the
portfolio's values will converge towards the true, although unknown, distribution. The VaR can be
easily inferred from the distribution, as we described above.
Monte Carlo simulation involves three steps.
First, Specify All the Relevant Risk Factors
Like the other approaches, we need to select all the relevant risk factors. In addition, we have to
specify the dynamics of these factors, i.e., their stochastic processes, and we need to estimate their
parameters (volatilities, correlations, mean reversion factors for interest rate processes, and so on).
For example, a commonly used model for stock prices is the geometric Brownian motion, which is
consistent with the Black-Scholes option-pricing model presented earlier in equation (3). It is
described by the stochastic differential equation (SDE):

Page 213
where Wt is a standard Wiener process and the drift, µ, and volatility, σ, are constant parameters that
need to be estimated using historical data. 36 The model assumes that the stock's rate of return is the
sum of a known deterministic ''drift" factor, µ, and an unknown factor, the "noise," which is drawn
from a normal distribution. The "noise," or innovations, dWt, in the stock price are assumed to be
uncorrelated over time, or more generally independent and identically distributed (i.i.d.), with dWt
being a random variable normally distributed with mean zero and variance dt. The random shock, or
innovation, at time t does not depend upon past information. This model is therefore consistent with
the efficient market hypothesis.
Geometric Brownian motion describes adequately the behavior of financial assets such as equities
and, to some extent, commodities, but it certainly does not describe the behavior of interest rates.
Interest rates exhibit mean reversion, and the drift term cannot be assumed to be constant. Hull
(2000) offers a detailed analysis of the stochastic processes followed by different classes of financial
assets (in particular, fixed-income securities).37
Second, Construct Price Paths
Geometric Brownian motion is one of the rare processes for which an explicit solution exists to SDE
(27), i.e.:
with Wt denoting the cumulative innovations from 0 to t.
To generate a discrete path of the underlying stock price, we apply (28) between two time instants, t
and t – 1:
where
∆t = time interval between t and t – 1
Z = standard normal variable N(0,1) such that
Price paths are constructed using random numbers produced by a random number generator.38 For a
simple portfolio without

Page 214
complex exotic options the forward distribution of portfolio returns at a 10-day horizon can be
generated in one step with ∆t = 10 days. Alternatively, if the simulation is performed on a daily basis
(i.e., ∆t = 1 day), a random distribution is drawn for each day to calculate the 10-day cumulative
impact.
When several correlated risk factors are involved, we need to simulate multivariate distributions.
Only in the case where the distributions are independent can the randomization be performed
independently for each variable as in (29). Suppose now that we want to generate the paths of n
multiple correlated assets, , each described by the process (27) with asset-specific drift
and volatility, µi and σi, and Wiener process .
If the instantaneous returns on securities i and j have correlation ρij, which means that
, then we can write the multivariate process as:
where X = (X1, . . . , Xn) is a multivariate normal with mean zero and covariance matrix Σ, such that
the i,j component is Σij = E(XXT) = ρij, which is symmetric, positive definite. 39
The process of generating a multivariate path starts with the generation of n independent standard
normal random variables, with mean zero and variance unity so that, E(YYT) = I,
where I is the identity matrix of dimension n with 1 on the diagonal and zeros elsewhere.
Next, construct the variables X =AY where A is a matrix such that Σ = AAT.40 We have thus generated
the desired correlated innovations from uncorrelated processes that are easy to produce.
As an example, consider the two-variable case. The covariance matrix can be decomposed into:
Then, if Y = (Y1, Y2) is a vector of independent unit-standard normal variables, the transformed
variables:

Page 215
that is,
have a covariance matrix Σ.
Third, Value the Portfolio for Each Path (Scenario)
Each path generates a set of values for the risk factors that are used as inputs into the pricing models,
for each security composing the portfolio. The process is repeated a large number of times, say
10,000 times, to generate the distribution, at the risk horizon, of the portfolio return. This step is
equivalent to the corresponding procedure for historical simulation, except that Monte Carlo
simulation can generate many more scenarios than historical simulation.
Then, VaR at the 99 percent confidence level is simply derived as the distance to the mean of the first
percentile of the distribution.
As is the case of historical simulation, a Monte Carlo simulation with full repricing requires the
analyst to specify the pricing models for each security in the portfolio. It is also possible to
implement a "hybrid" Monte Carlo simulation where the pricing model is replaced by the Taylor
expansion (delta-normal or delta-gamma-vega-rho-theta method) that is used in the variance-
covariance approach. This hybrid technique presents the advantage of being less computer intensive.
Monte Carlo simulation is a powerful and flexible approach to VaR. It can accommodate any
distribution of risk factors to allow for "fat tail" distributions, where extreme events are expected to
occur more commonly than in normal distributions, and "jumps" or discontinuities in price processes.
For example, a process can be described as a mixture of two normal distributions, or as a jump-
diffusion process (both processes are consistent with fat tails).
As we mentioned above, other distributions, such as the Student-t distribution, are also often
suggested as ways to generate heavy tails. Also, as noted by Broadie and Glasserman (1998), the
four-parameter family of Ramberg et al. (1979) provides enough flexibility to match a wide range of
values of skew and kurtosis. It can also accommodate complex portfolios that contain exotic options.
For example, the approach can cope with path-dependent

Page 216
options such as Asian options and barrier options, the value of which depends on the path followed by the underlying factors.
Monte Carlo, like historical simulation, allows the analyst to calculate the confidence interval of VaR, i.e., the range of likely values that
VaR can take if we had to repeat many times the Monte Carlo simulation. The narrower this confidence interval, the more precise is the
estimate of VaR. In the case of Monte Carlo simulation, however, it is easy to carry out sensitivity analyses by changing the market
parameters used in the analysis—such as the term structure of interest rates.
The major limitation of Monte Carlo simulation is the amount of computer resources it usually requires. Variance reduction techniques can
be used to reduce the computational time, such as the antithetic technique, the control variates approach, quasirandom sequences, and other
methods of stratification. 41 Still, Monte Carlo simulation remains very computer intensive and cannot be used to calculate the VaRs of
very large and complex portfolios. At most, it can be used for portfolios of a limited size.42
5—
Conclusion:
Pros and Cons of the Different Approaches
Each of the approaches we have described has advantages and limitations: no single technique dominates the others. Tables 5.10a–c
summarize the pros and cons of the different approaches.
TABLE 5.10a
Pros and Cons of the Variance-Covariance Approach
Pros Cons
Computationally efficient: it takes only a few minutes to run the position of Assumes normality of the return portfolio.
the entire bank.
Because of central limit theorem, the methodology can be applied even if the Assumes that the risk factors follow a multivariate log-normal distribution,
risk factors are not normal, provided the factors are numerous and relatively and thus does not cope very well with "fat tail" distributions.
independent.
(continued)

Page 217
(continued)
TABLE 5.10a
Pros and Cons of the Variance-Covariance Approach
Pros Cons
No pricing model is required: only the Greeks are necessary, and these can be Requires the estimation of the volatilities of the risk factors as well as the
provided directly by most of the systems that already exist within banks (i.e., correlations of their returns.
the legacy systems).
It is easy to handle incremental VaR. Security returns can be approximated by means of a Taylor expansion. In
some instances, however, a secondorder expansion may not be sufficient to
capture option risk (especially in the case of exotic options).
Cannot be used to conduct sensitivity analysis.
Cannot be used to derive the confidence interval for VaR.
TABLE 5.10b
Pros and Cons of the Historical Simulation Approach
Pros Cons
No need to make any assumption about the distribution of the risk factors. Complete dependence on a particular historical data set and its idiosyncrasies.
That is, extreme events such as market crashes either lie outside the data set
and are ignored, or lie within the data set and (for some purposes) act to distort
it.
No need to estimate volatilities and correlations: they are implicitly captured Cannot accommodate changes in the market structure, such as the introduction
by the actual (synchronous) daily realizations of the market factors. of the Euro in January 1999.
Fat tails of distributions, and other extreme events, are captured so long as Short data set may lead to biased and imprecise estimation of VaR.
they are contained in the data set.
Aggregation across markets is straightforward. Cannot be used to conduct sensitivity analyses.
Allows the calculation of confidence intervals for VaR. Not always computationally efficient when the portfolio contains complex
securities.

Page 218
TABLE 5.10c
Pros and Cons of the Monte Carlo Simulation Approach
Pros Cons
Can accommodate any distribution of risk factors. Outliers are not incorporated into the distribution.
Can be used to model any complex portfolio. Computer intensive.
Allows the calculation of confidence intervals for VaR.
Allows the user to perform sensitivity analyses and stress testing.
Appendix 1—
Duration and Convexity of a Bond
Bonds typically promise their holders payments every six months during the life of the agreement. This stream of cash
flows is fully characterized by the:
• Maturity of the bond, n, at which time the principal, or face value, of the bond, F, is paid and the bond is retired.
• Coupon rate, c, expressed as an annual rate of return; the annual cash flow is cF, and therefore, cF/2 is the semi-
annual coupon paid every six months until maturity.
The entire income stream on a typical bond can then be represented by the 2n payments:
For bonds paying an annual coupon, cF, there are n annual payments:
For the sake of simplicity, we will limit the following analysis to annual coupon bonds, while the generalization to semi-
annual coupon bonds is straightforward. 43

Page 219
A1—
Valuation of a Bond and Yield to Maturity
The present value of a bond is determined by:
• Its stream of future cash flows, which consist of the n annual coupon payments, cF, during the life
of the bond and the repayment of principal, F, at maturity, n
• Its discount curve, or zero-coupon curve, which specifies the spot rates, R1, R2, . . . , Rn, at which
each cash flow should be discounted to produce its present value.
The first coupon payable in one year has a present value of cF/(1 + R1). Similarly, the coupon payable
in two years has a present value of cF/(1 + R2)2. The bond has a present value that is the sum of the
present values of its future cash flows:
To define the duration of the bond, we need first to derive its yield to maturity, y, which satisfies the
relation:
In other words, y is the single rate of interest that makes the present value of the future cash flows
equal to the price of the bond. This single rate is used to discount all the cash flows. It is only when
the spot zero curve is flat (i.e., all the spot zero-coupon rates are the same across all maturities, and
equal to R) that the yield to maturity, y, is equal to the level of interest rate, R.
Numerical Example
The following term structure of interest rates applies to a three-year bond that pays an annual coupon
of 4 percent and has a nominal value of $100:
t 1 2 3
Rt (%) 3 3.75 4.25
Then, according to (A3), the price of the bond is:

Page 220
The yield to maturity, y, is the solution of (A4), i.e.:
which gives y = 4.22 percent.
A2—
Duration of a Bond
Given the pricing equation for a bond (A4), the duration is defined as the weighted average of the
dates (expressed in years) of each cash flow, where the weights are the present value of the cash
payment divided by the sum of the weights, i.e., the price of the bond itself:
Note that the sum of the weights in (A7) is equal to one, i.e.:
since the numerator of (A8) is, according to (A4), the price of the bond.
Numerical Example (Continuation)
Consider the three-year bond presented in (A5). Its duration is:
Properties of the Duration 44
From the definition of duration in (A6), it follows that its value depends on the maturity, the coupon,
and the yield to maturity of the bond. More specifically:
• The duration of a bond is always less than its maturity, except for a zero-coupon bond where it is
exactly equal to

Page 221
the maturity of the unique bullet payment of the bond at maturity. In general, increasing the maturity
of a bond will also increase its duration. This is always true for bonds trading at a premium, i.e., when
the coupon is higher than the yield to maturity. It is not always the case for long-term discount bonds
with a coupon lower than the yield to maturity.
• Increasing the coupon of the bond, while keeping the maturity and the yield constant, reduces the
duration of the bond. Indeed, bonds with higher coupons distribute relatively more of their cash flows
sooner and, therefore, have a shorter average life.
• Increasing the yield to maturity of a bond, while keeping the maturity and the coupon rate constant,
reduces the duration of the bond. Indeed, a higher discount rate implies a lower discount factor, and
therefore a lower weight for remote cash flows, and consequently a shorter average life.
A3—
Duration as a Measure of Interest Sensitivity
Simple differentiation of equation (A4), which relates the bond price to its yield to maturity, yields:
where ∆P is the change in price corresponding to a change in yield ∆y, and
D is known as Macaulay duration after the name of the economist Frederick R. Macaulay who in
1938 first coined this term. D* as defined in (A10) is called "modified duration."
According to (A9) there is a linear relationship between the change in price of a bond and the change
in yield. The higher the duration, the higher the price volatility. However, as the price-yield
relationship for a bond is nonlinear, duration is only a first-order approximation of the impact of a
change in yield on the price of a

Page 222
Figure A5.1
Duration As a Measure of Interest Rate Sensitivity
bond. This means that it only offers a good approximation for small variations in yield (Figure A5.1).
Numerical Example (Continuation)
Assume a change of 10 bp in the yield of the three-year bond defined by (A5) and (A6) with a price P
= 99.39, a duration D = 2.89, and a yield y = 4.22%. Then, according to (A9):
A4—
Duration and Risk
According to (A9), ∆P = –PD*∆y, so that:
The volatility of the change in bond prices is equal to the product of the modified duration and the
bond price, times the volatility of the yield.

Page 223
Numerical Example (Continuation)
Assume that the daily changes in yield for the three-year bond are normally distributed, with a daily
volatility of 4 bp (0.04 percent). Then:
So that VaR at the 99 percent confidence level is:
A5—
Convexity Adjustment to Interest Rate Sensitivity
The Taylor expansion at the second-order level of the bond price formula is:
If we neglect the third-order error term, (A11) can be rewritten as:
so that:
or,equivalently:
The first term in (A13) is identical to (A9). The second term is the convexity adjustment where
denotes the convexity of the bond. A good numerical approximation of convexity is given by:
where the change in yield ∆y is set to 1 bp, i.e., 10–4.

Page 224
Figure A5.2
The convexity adjustment in (A13) compensates for the change in the slope of the price-yield curve,
when the yield changes are substantial (see Figure A5.2).
Numerical Example
We can measure convexity as:
Example:

Page 225
A6—
Limitations and Extensions of the Duration Model
The duration model assumes there is only one risk factor—the yield to maturity of the bond. It also
implicitly assumes that the yield curve is flat, and that any interest rate shock will cause a parallel
shift on the yield curve. The reality is different. The yield curve is not flat, and interest rates are
imperfectly correlated. When there is a shock, interest rates along the yield curve are affected
differently.
To capture this feature, we need a model with several risk factors, each factor being a key rate on the
yield curve. 45
Notes
1. This claim is based on the famous interest rate parity condition (see, for example, Van Horne,
1994).
2. A famous example is Caterpillar, a U.S. heavy equipment firm, which began in 1987 a $2 billion
capital investment program. A full cost reduction of 19 percent was eventually expected in 1993.
During the same period the Japanese yen weakened against the U.S. dollar by 30 percent, which
placed Caterpillar at a competitive disadvantage vis- -vis its major competitor, Komatsu of Japan,
even after adjusting for productivity gains.
3. The press is full of stunning examples of corporations that have incurred major foreign exchange
transaction losses. See, e.g., Ahn and Falloon (1991).
4. Exceptional shocks means price and/or rate changes that are not consistent with the assumptions
about the distributions of the risk factors as, for example, a price change 10 standard deviations away
from its historical mean, when the distribution is assumed to be normal. Such a ''jump" in price is
inconsistent with the assumption of normality since its probability of occurrence under the normality
assumption is very close to zero.
5. For example, it is common to make the assumption that stock prices are log-normally distributed in
order to facilitate the modeling of risk in an equity portfolio.
6. DV01 is a trader's abbreviation for the change ("delta") in value consecutive to a change in yield of
one basis point, i.e., 1 percent of a percentage point.
7. Macaulay (1938) first used the term "duration," and derived the first duration formula as a measure
of the average life of a security.

Page 226
8. See also Chapter 1, Section 4.
9. Many publications offer a good overall presentation of VaR, e.g., Dowd (1998), Fallon (1996),
Jorion (1996a, 1996b), Linsmeier and Pearson (1996), and Phelan (1995).
10. A multiplier of 3 is applied to derive regulatory capital (Chapter 4, Section 3.1).
11. According to the statistics produced by KMV (see Chapter 9) the actual probability of default of
an AA company is about 4 bp.
12. In statistics the standard deviation is a measure of the dispersion of a random variable. VaR is a
generalization of this measure to any portfolio of securities whose individual prices may be
influenced by many risk factors with correlated probability distributions.
13. Note that this definition is not satisfactory since it compares values at different time instants, the
current time and the risk horizon, H. There is an element of inconsistency in this definition. Instead,
VaR focuses on the forward distribution of the value of a position, or alternatively on the forward
distribution of the portfolio returns, and then derives the forward maximum loss at the risk horizon at
a given confidence level. Only expression (6) is consistent with this view.
14. CIBC's value-at-risk system is described in terms of "risk management units (RMUs). For
example, a trading position that has 1 RMU of risk has a 1 percent chance of losing more than $1000
over a one-day period.
15. The use of derivatives on the portfolio components, or derivatives on broad indices, may also
introduce significant deviation from the normal distribution.
16. See, e.g., Abramowitz and Stegum (1970) and Johnson et al. (1995).
17. See, e.g., Diebold et al. (1998), who illustrates the fallacy of the scaling the one-day VaR by the
square root of time when volatility follows a GARCH process.
18. VaR should be reported not only for the aggregate portfolio, but also for each business unit in the
tree hierarchy of the firm. In addition, VaR should also be reported by risk factor and/or combination
of risk factors.
19. The generalized variance-covariance approach for nonlinear products such as derivative products
is presented in Chapter 6.
20. A tractable alternative consistent with fat tails would be to assume that the portfolio return is
distributed as Student-t (see Section 3.2.2).
21. The generalization to N assets, or N risk factors, is staightforward.

Page 227
22. We assume that stock prices are adjusted for dividend in the return calculation; i.e., the stock
price at time t is the price ex-dividend plus any dividend paid out in the period t–1, t.
23. A portfolio is said to be linear in risks when the change in the value of the portfolio is a linear
expression of the risk factors. This is precisely the case for a stock portfolio where the risk factors are
the rates of return on each individual stock. Then, according to (13), , where N
denotes the number of stocks in the portfolio.
24. Note that niSi = ωiV for all stock i.
25. In the delta-normal approach we neglect the convexity adjustment term in dy2 which is
nonnormally distributed (see Chapter 6). The goodness of the delta-normal approximation depends on
the length of the time period. The smaller the time period, the smaller the change in dy and, hence,
the smaller the squared change dy2. The delta-normal approximation is only legitimate for relatively
short holding periods.
26. See, for example, Hull (2000, Chapter 3).
27. A storage cost can be viewed as a negative dividend yield. In some instances, the holder of some
commodities benefits from holding physically the commodity because it can provide her/him with a
competitive advantage if there is a shortage in supply in the future. The forward price incorporates
this benefit in the form of a "convenience" yield which can be interpreted as an implicit dividend.
28. It is the well-known "cash and carry" equation (see Hull 2000, Chapter 3).
29. We have omitted the time subscript to simplify the notation.
30. Alternatively, order the resulting portfolio value changes from smallest to greatest and locate the
change corresponding to the desired percentile. For example, if 500 days of historical data are used,
the first percentile is given the fifth smallest change in the portfolio.
31. This example is taken from lecture notes at the CIBC School of Derivatives.
32. In fact, an alternative to historical simulation with full repricing is "hybrid" historical simulation
where portfolio returns are derived from a Taylor expansion of the pricing models, as in the variance-
covariance approach (delta-normal or delta-gamma-vega-rho-theta approach).
33. This example is taken from lecture notes at the CIBC School of Derivatives.

Page 228
34. This statement is too strong in some instances, such as in our example, where we use Black-
Scholes formulas to value the options.
35. An excellent reference to the Monte Carlo simulation approach and its application to the pricing
of securities and risk management is Broadie and Glasserman (1998).
36. For the purpose of risk management we need to simulate the actual distribution of the risk factors,
so that µ represent the actual instantaneous expected return. However, when pricing securities using
Monte Carlo simulation, we need to use the risk neutral distribution for which the expected return µ
= r, where r is the instantaneous risk-free rate of interest.
37. It should be noted that over a short horizon, such as 10 days, we can omit mean reversion, even
for bonds, in the modeling of the risk factors since mean reversion plays a role only over longer
periods of time.
38. See Broadie and Glasserman (1998) for a detailed exposition of random number generation. In
some cases these paths are generated using what is called "pseudo-random" numbers that do not
mimic real random numbers as such, but instead attempt to fill the domain interval more uniformly
and avoid the clusters that often occur with random numbers. This technique is very often used for
high-dimensional problems.
39. We can then use the so-called Cholesky decomposition of the covariance matrix, i.e., express the
covariance matrix as the product, Σ = AAT, where A is a lower triangular matrix with zeros on the
upper right part, and AT denotes its transpose.
40. The covariance matrix of X is E(AYYT AT) = AE(YYT)AT = AIAT = AAT = Σ.
41. See, e.g., Broadie and Glasserman (1998).
42. Other approaches, such as Monte Carlo simulation with interpolation as proposed by Jamshidian
and Zhu (1997), can be used.
43. See, e.g., Bierwag (1987), Tuckman (1995), and Fabozzi (1997).
44. For a detailed account of the properties of the duration of a bond, see Bierwag (1987) and
Garbade (1996).
45. See, e.g., Schaefer (1986) and Ho (1992). An alternative to building a multifactor model is
proposed by Litterman and Scheinkman (1988), who base their approach on factor analysis.

Page 229
Chapter 6—
Measuring Market Risk:
Extensions of the VaR Approach and Testing the Models
1—
Introduction
Value at risk (VaR) is far from being a perfect measure of risk. One problem is that it aggregates the
various components of risk into a single number. This is very useful when estimating the overall risk
of an institution. But risk managers need to find out which of the component risks contribute most to
the total risk. This is the purpose of the "Incremental-VaR" and "DeltaVaR" measures that are
presented in the second section of this chapter.
To facilitate the implementation of a VaR model, it is common to assume that market conditions will
remain normal, that is, that they will be characterized by risk factors that are lognormally distributed,
with stationary expected returns and standard deviations. This does not reflect reality. In the third
section of this chapter we therefore look at stress testing and scenario analysis. These methodologies
can be used to analyze extreme events that lie outside normal market conditions.
Methodologies of this kind are important because we do not know how to construct a VaR model that
would combine, in a meaningful way, periods of normal market conditions with periods of market
crises characterized by large price changes, high volatility, and a breakdown in the correlations
among the risk factors.

Page 230
Another problem is that VaR is usually calculated within a static framework and is therefore not
suitable for the incorporation of liquidity risk. It is only appropriate for relatively short time horizons.
In the fourth section of the chapter we propose a dynamic VaR framework with which to assess the
risk of portfolios over long time horizons.
As a statistical measure, VaR must be expressed in conjunction with an error term, or confidence
interval. The fifth section of the chapter shows how to derive confidence intervals for VaR figures
that have been calculated using historical and Monte Carlo simulations.
In order to produce timely risk reports, a VaR model must be both accurate and computationally
efficient. To this end, the sixth section of the chapter introduces an extension of the DeltaVaR 1
model that we first presented in Chapter 5.
The VaR measure helps risk managers describe risk in terms of a loss level that might be breached
on, say, one day in every 100 trading days. But it does not tell the manager anything about the
magnitude of the potential loss in the tail of the distribution. In the final section of this chapter we
propose an alternative risk measure: extreme value at risk or EVaR. This measure represents the
expected loss in the tail of the portfolio distribution, provided that the loss is greater than VaR.
2—
Incremental-VaR (IVaR), DeltaVar (DVaR), and Most Significant Risks
A key concern in risk management is the identification of the primary sources of risk in complex
portfolios, and the hedging trades that will reduce those specific risks.2 To achieve this, the portfolio
VaR must be decomposed to determine the impact of individual instruments, or positions, on the
overall VaR.
This is more complicated than it sounds since each position's contribution to the total risk of the
portfolio depends on the composition of the portfolio. More specifically, it depends on how closely
the position values are correlated with the values of other assets in the portfolio.

Page 231
Two complementary measures can be used to investigate this: "Incremental-VaR" (IVaR) and
"DeltaVaR" (DVaR).
2.1—
Incremental-VaR (IVaR)
Incremental-VaR, or IVaR, measures the incremental impact on the overall VaR of the portfolio of
adding or eliminating an asset, A, or a position:
IVaR (A) can be positive if the asset is positively correlated with the rest of the portfolio and thus
adds to the overall risk. Or it can be negative, if the asset is a hedge against existing risks in the
portfolio, i.e., if it is negatively correlated with the rest of the portfolio.
The implementation of (1) is relatively straightforward and it can be calculated quite quickly when
the methodology adopted for calculating VaR is based on the variance-covariance approach (Chapter
5).
2.2—
DeltaVaR (DVaR) 3
DeltaVaR, or DVaR, measures the risk contribution of an asset to the overall risk of the portfolio.
The sum of the risk contributions is equal to the overall risk of the portfolio. DeltaVaR depends on
the composition of the portfolio and the correlation structure of the assets. Consider a portfolio, P,
composed of N assets, i = 1, . . . , N; pi and Ai are, respectively, the unit price and the number of units
of asset i in the portfolio. The portfolio value is:
The DeltaVaR property is:

Page 232
The total VaR of the portfolio is the sum of the risk contributions, DVaRi, of all the assets contained
in the portfolio. 4 This is a useful decomposition since it highlights the "most significant risks," i.e.,
the positions to which the portfolio is most sensitive.5
DVaRi is the product of the marginal change in risk per unit change in asset i, and the position size
itself. DVaRi represents the risk contribution of asset i to the portfolio.
Once the most significant risks have been recognized, the next step is to identify the hedge portfolios
that can optimally reduce these risks, given hedging costs. These optimal hedge portfolios can be
derived as the solution of an optimization problem.
3—
Stress Testing and Scenario Analysis
The purpose of stress testing and scenario analysis is to determine the size—though not the frequency
—of potential losses related to specific scenarios. A scenario may consist of extreme changes in the
value of a risk factor (interest rate, credit spread, exchange rate, equity price, or commodity price)
such as a shift of 100 bp in the level of interest rates over the period of a month. The calculation that
tells us how much the portfolio might lose in such a scenario is known as a "stress test."
A scenario might also correspond to extreme historical events such as the stock market crash of
October 1987. On October 19, 1987, stock prices fell by 23 percent in the United States, or
approximately 22 times their daily standard deviation. Other historical scenarios might include the
failure of the European exchange rate mechanism in September 1992, or the tightening of monetary
policy by the Federal Reserve in the United States in May 1994 (and the subsequent fall in bond
prices).
Regulators view stress testing and scenario analysis as a necessary complement to the use of internal
VaR models. Indeed, as VaR is a statistical model, its implementation requires banks to make
simplifying assumptions about risk factors, e.g.:
• Their number is most often dictated by the availability of data; for instance reliable data for implied
volatilites can only be obtained for short maturities.

Page 233
• The joint probability distribution of their rate of return: it is common practice to assume that the risk
factors are log-normally, or normally, distributed, i.e., have a "smooth" behavior that excludes the
possibility of jumps and other extreme events.
These simplifying assumptions are necessary to run computationally efficient models. They also
reflect what are called "normal market conditions," i.e., those for which we have enough data to
estimate volatilities and correlations. In the real world, however, we sometimes observe extreme
events that correspond to price variations that are quite inconsistent with the normal distribution.
The Derivative Policy Group (1995) recommended specific guidelines for stress testing:
• Parallel yield curve shift of plus or minus 100 bp
• Yield curve twist of plus or minus 25 bp
• Equity index changes of plus or minus 10 percent
• Currency changes of plus or minus 6 percent
• Volatility changes of plus or minus 20 percent
These extreme price and rate variations may dramatically affect the value of a portfolio with strong
nonlinearities and large negative gammas. Portfolios of this kind incur losses whether prices fall or
rise, and the magnitude of the losses accelerates as the change in price increases. (Gamma is the
nickname for the second derivative of the instrument's value with respect to the value of the
underlying asset.)
The regulators also require that financial institutions run scenarios that capture the specific
characteristics of their portfolios, i.e., scenarios that involve the risk factors to which their portfolios
are most sensitive. Following the market crisis of the summer of 1998, when the disappearance of
liquidity in some financial markets led to several well-publicized losses, 6 regulators require financial
institutions to include "liquidity risk" in their scenario analyses.
3.1—
Stress Testing
At CIBC, a new methodology named "stress envelopes" has been developed. Stress envelopes are
produced by combining stress

Page 234
TABLE 6.1
Stress Categories and the Number of Stress Shocks
Stress Category Stress Shock
1 Interest rates 6
2 Foreign exchange 2
3 Equity 1
4 Commodity 2
5 Credit spreads 1
6 Swap spreads 2
7 Vega (volatility) 2
categories with worst possible "stress shocks," across all possible markets for every business.
The methodology employs seven stress categories: interest rates, foreign exchange rates, equity prices,
commodity prices, credit spreads, swap spreads, and vega (volatility). For each stress category, the worst
possible stress shocks that might realistically occur in the market are defined. In the case of interest rates,
for example, the methodology defines six stress shocks to accommodate both changes in the level of rates
and changes in the shape of the yield curve. In the case of credit spreads and equities there is only one
stress shock, i.e., the widening of credit spreads and the fall of equity prices, respectively. All other stress
categories make use of two stress shocks—spreads or prices increase or decrease as shown in Table 6.1.
A stress envelope is the change in market value of a business position in a particular currency or market, in
response to a particular stress shock. A scenario is a combination of several stress shocks (Figure 6.1).
The following example illustrates how the stress envelope methodology works. Consider the following
scenario:
1. 10 percent fall in the North American equity indices
2. 15 percent fall in European equity indices
3. a fall of 50 bp in North American short-term interest rates

Page 235
Figure 6.1
The Seven Major Components of the Stress Envelope Approach
The components of the scenarios are first related to the corresponding extreme stress shocks and their
stress envelope values:
1. 25 percent fall in the North American equity indices
2. 25 percent fall in European equity indices
3. a fall of 200 bp in North American short-term interest rates
The impact of the scenario on the position is then derived by summing the appropriate percentage
(less than one) of the stress shock values, for each of the three stress shocks (Table 6.2).
The linear interpolation in the calculation of the scenario value, with the scenario value being the
worst case stress envelope value times the scenario shock weight, is rather conservative. For
nonlinear positions, the situation that concerns banks most is when gamma is negative, i.e., when the
position experiences a loss whether the price of the underlying instrument moves up or down.

Page 236
TABLE 6.2
Stress Scenario
Stress Envelope Stress Envelope Scenario Shocks Scenario Shock Scenario
Values Shocks Weights Values
1 ($1,000) 25% 10% 10/25 = 40% ($400)
2 ($500) 25% 15% 15/25 = 60% ($300)
3 $700 200 bp 50 bp 50/200 = 25% $175
Total = ($525)
Note: The scenario value is the product of the stress envelope value and scenario shock weight (less than one). The
scenario shock weight is the ratio of the scenario shock to the stress envelope shock.
Numbers in parentheses are negative values.
For this situation, the scenario value derived using the methodology described above will overestimate
the actual loss, since with negative gamma the magnitude of the loss accelerates with the size of the
price change.
3.2—
Summary of the Most Significant Risks
The stress testing methodology presented in the previous section can be combined with the VaR
approach to produce a ''summary of significant risks." This report ranks the risk exposure of the bank's
positions. For each position, it shows the VaR, IVaR, and DVaR and the loss corresponding to the
stress scenario that would affect the position the most. For example, the high-yield portfolio might
well be most exposed to a widening of credit spreads. Therefore the relevant scenario corresponds to
the stress envelope for a widening of credit spreads.
3.3—
Scenario Analysis
At CIBC, two types of scenarios are run: replication scenarios that attempt to reproduce the effects of
extreme historical events and hypothetical one-off events that depend on imagined future
developments.

Page 237
(i)—
Replication Scenarios
Scenario 1: Stock market crash reminiscent of the October 1987 crash, characterized by a
combination of the following events:
• Equity markets fall around the globe by 20 percent on average, with Asian markets, such as Hong
Kong, declining by 30 percent, and an upward shift in implied volatilities from 20 to 50 percent.
• The U.S. dollar rallies against other currencies as a consequence of a flight to quality. Asian
currencies lose up to 10 percent against the dollar.
• Interest rates fall in Western markets. Hong Kong interest rates rise by 40 bp at the long end of the
term structure and by 100 bp at the short end.
• Commodity prices drop due to fears of a recession: copper and oil prices decline by 5 percent.
Scenario 2: U.S. inflation scare and a tightening of monetary policy by the Federal Reserve as in May
1994, characterized by:
• 100-bp increase in overnight interest rate and 50-bp upward shift in the long end of the curve.
• Interest rates also increase in other G-7 countries and Switzerland, but not as much as in the United
States.
• G-7 currencies depreciate against the U.S. dollar as investors chase higher rates.
• Credit spreads widen.
• Equity markets decline from 3 to 6 percent with an upward shift in implied volatilities.
Scenario 3: Japanese earthquake:
• Japanese equity markets drop by 15 percent and other equity markets fall less sharply (Canada and
the United States by 5 percent).
• Yen falls 3 percent against the U.S. dollar, and the U.S. dollar also appreciates slightly against
other currencies.
• Interest rates rise in Europe and the United States through fear of the repatriation of Japanese funds.

Page 238
(ii)—
Hypothetical One-Off Scenarios
• Canada crisis: "Yes" scenario at a referendum on the separation of Quebec from the rest of Canada.
• Credit spreads widen.
• Swap spreads widen or narrow.
• Chinese devalue their currency, which causes a crisis in Asia.
3.4—
Worst Case Scenario Analysis
The kind of analysis we have just described complements the VaR approach. It determines the worst
case losses for various extreme scenarios for which the underlying distribution of the risk factors
deviates substantially from standard log-normality. An alternative approach to stress testing and
scenario analysis is the "worst case scenario" analysis proposed by Boudoukh et al. (1995).
Like the VaR approach, such a worst case scenario analysis assumes that portfolio returns are
normally distributed, with mean return µP and standard deviation σP. The fundamental difference
between the two techniques is that while VaR expresses the price risk of a portfolio in terms of the
frequency of a specific level of loss, worst case scenario analysis asks the question, "What is the
worst that can happen to the value of the portfolio over a given period of time?"
Formally, to implement the worst case scenario we derive numerically the probability distribution of
the maximum loss over a period of length H, say 250 days, i.e., F[min(Z1, Z2, . . . , ZH)], where F[.]
denotes the distribution function and Zi is the normalized return of the portfolio in day i. The focus is
on the worst daily scenarios.
Table 6.3 shows the values of the expected loss in the worst case scenario analysis (expected WCS)
for different horizons H = 5, 20, 100, and 250 days. The first percentile of the distribution of the
minimum is also reported. Both the expected worst case loss and the first percentile of the worst case
loss distribution are derived from a Monte Carlo simulation with 10,000 runs. For example, assuming
a mean portfolio return of zero, VaR at the 99 percent confidence level is 2.33 σP. When the horizon
is 250 days, i.e.,

Page 239
TABLE 6.3
Worst Case Scenario Analysis
Horizon (days)
5 20 100 250
E[number of Zi<–2.33] 0.05 0.20 1.00 2.50
Expected WCS –1.16 –1.86 –2.51 –2.82
First percentile of Z –2.80 –3.26 –3.72 –3.92
The worst case scenario (WCS), i.e., min(Z1, Z2, . . . , ZH), denoted Z, is defined as the lowest observation in a vector
Z = (Z1, Z2, . . . , ZH) of length H = 5, 20, 100, and 250 days of independent draws. These draws are normally
distributed with mean 0 and volatility 1.
Source: Boudoukh et al. (1995), Risk 8(9).
one year, the expected worst case loss is 2.82 σP and the first percentile of the worst case loss is 3.92
σP.
In other words, while there is a 1 percent chance that actual losses in any trading day will exceed 2.33
σP, there is a probability of 1 percent that the size of the worst case loss will be greater than 3.92 σP in
any given year. In other words, one year every 100 years, on average, the worst case daily loss will be
greater than 3.92 σP. The same methodology can be applied to fixed-income products and derivatives.
Worst case scenario analysis is therefore more conservative than VaR. If an institution bases its
economic capital on VaR, it will have enough capital to avoid loss on 99 percent of days. However, a
more conservative approach might be to set aside capital that will absorb the worst case loss over a
given period of time, say one year. In the context of the previous example, the worst case scenario
approach would require the bank to hold 1.68 (= 3.92/2.33) times more capital than would the VaR
approach.
3.5—
Advantages of Stress Testing and Scenario Analysis
The major benefit of stress testing and scenario analysis is the identification of the vulnerability of a
portfolio to a variety of extreme events. During a market crisis, historical correlations change as

Page 240
volatilities increase. Correlations may suddenly increase dramatically and become +1, as many
markets collapse at the same time, and liquidity dries out. Alternatively, correlations may approach –
1 as markets or instruments move in opposite directions. For example, a market